Wave Characteristics and Equations Quiz
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Questions and Answers

Which wave among Wave 1, Wave 2, and Wave 3 has the greatest wave speed?

  • All waves have the same speed
  • Wave 2 (correct)
  • Wave 3
  • Wave 1

Which wave has the greatest maximum transverse string speed?

  • None of the waves have a maximum speed
  • Wave 1 (correct)
  • Wave 3
  • Wave 2

If the angular frequency of a wave increases, what happens to its wave speed?

  • It increases (correct)
  • It remains constant
  • Cannot be determined
  • It decreases

What is the relationship between wave speed and angular frequency?

<p>Directly proportional (D)</p> Signup and view all the answers

Which wave has the lowest amplitude?

<p>Wave 1 (2 cm) (A)</p> Signup and view all the answers

Which statement is correct regarding the characteristics of the waves?

<p>Wave 2 travels faster than Wave 1 (D)</p> Signup and view all the answers

What can be inferred about the waves if they are travelling in the same medium?

<p>Wave speeds will vary (B)</p> Signup and view all the answers

If the wavelength of a wave increases, what happens to its wave speed in the same medium?

<p>It increases (C)</p> Signup and view all the answers

What type of waves are produced by a motorboat sailing on water?

<p>Both Longitudinal and Transverse (B)</p> Signup and view all the answers

Which statement correctly describes the phases at points A and B when waves are produced by a motorboat?

<p>The phase at A is greater than the phase at B (A)</p> Signup and view all the answers

What is the linear density of a string if it is given as 1.3 × 10–4 kg/m?

<p>1.3 × 10–4 kg/m (A)</p> Signup and view all the answers

Which formula correctly describes the velocity of sound in gases?

<p>v = \sqrt{\frac{p}{\rho}} (D)</p> Signup and view all the answers

At room temperature, the speed of sound in air is proportional to which of the following?

<p>Square root of atmospheric pressure (C)</p> Signup and view all the answers

If the velocity of sound in moist air is $ u_m$ and in dry air is $ u_d$, then which is true?

<p>$\nu_m &gt; \nu_d$ (A)</p> Signup and view all the answers

What is the ratio $ rac{I}{I_0}$ for a sound intensity level of 30 dB?

<p>1000 (D)</p> Signup and view all the answers

In a sine wave with amplitude A and wavelength λ, what symbolizes the wave velocity?

<p>V (D)</p> Signup and view all the answers

The velocity of sound in a gas depends on which of the following?

<p>On the density and elasticity of gas (B)</p> Signup and view all the answers

If at a certain point the amplitude of sound doubles and the frequency becomes one fourth, what happens to the intensity of sound?

<p>Becomes one fourth (C)</p> Signup and view all the answers

What will happen to the frequency and wavelength of sound when it moves from water to air?

<p>Frequency remains the same; wavelength decreases (C)</p> Signup and view all the answers

A sings with a frequency (n) and B sings with a frequency 1/8 that of A. If the amplitude of A is 'a', what will be the amplitude of B?

<p>8a (D)</p> Signup and view all the answers

In two monoatomic gases with densities $ ho_1$ and $ ho_2$, if $ ho_1 = 4$ and the velocities of sound are $v_1$ and $v_2$ respectively, which relation holds true?

<p>$ rac{v_1}{v_2} = 2$ (C)</p> Signup and view all the answers

If sound travels in water at 1450 m/s and in air at 330 m/s, when transitioning from water to air, what effect occurs?

<p>Decreased frequency, increased wavelength (A)</p> Signup and view all the answers

Which relationship correctly represents the frequency $ u$ of a wave in relation to its wavelength $ ext{λ}$?

<p>$ u = rac{c}{ ext{λ}}$ (D)</p> Signup and view all the answers

The time period of simple harmonic motion (SHM) for a particle is given as 12 s. What is its frequency?

<p>$ rac{1}{12}$ Hz (A)</p> Signup and view all the answers

What is the fundamental frequency that can be excited in a tube open at both ends based on the provided options?

<p>512 Hz (A)</p> Signup and view all the answers

How long is the air column in a closed pipe that resonates with a tuning fork of frequency 264 Hz?

<p>31.25 cm (A)</p> Signup and view all the answers

What is the velocity of sound if two closed organ pipes of lengths 0.750 m and 0.770 m produce 3 beats per second?

<p>346.5 m/sec (A)</p> Signup and view all the answers

What is the minimum length of a tube open at both ends that resonates with a tuning fork of frequency 350 Hz?

<p>50 cm (C)</p> Signup and view all the answers

What is the apparent change in pitch of sound due to relative motion between the observer and the source called?

<p>Doppler's effect (A)</p> Signup and view all the answers

If a siren emits waves of frequency 1000 Hz and a car driver approaches at 90 km/hour, what frequency is heard by the driver?

<p>1076 Hz (A)</p> Signup and view all the answers

What is the highest overtone that can be excited in a closed pipe?

<p>Second overtone (C)</p> Signup and view all the answers

What is the frequency of the underwater sonar source operating at 60 kHz directed towards the surface?

<p>60000 Hz (C)</p> Signup and view all the answers

Which frequency corresponds to the sound that the closed pipe can resonate?

<p>80 Hz (C), 240 Hz (D)</p> Signup and view all the answers

Identify the wave equation with the highest amplitude from the given options.

<p>y = (4mm) sin(10x - 20t) (B)</p> Signup and view all the answers

Which wave disturbance describes a wave function given as y(x, t) = 0.02 cos(50πt + π/2) cos(10πx)?

<p>A standing wave (A)</p> Signup and view all the answers

In the wave displacement equations provided, which has the simplest form with no coefficients mentioned?

<p>y = (1mm) sin(8x - 16t) (C)</p> Signup and view all the answers

What frequency will an observer hear if a source of sound with a frequency of 500 Hz is moving towards them at 30 m/s, with the speed of sound being 330 m/s?

<p>550 Hz (C)</p> Signup and view all the answers

How many beats will be heard by a passenger in a bus moving towards a wall when a horn of frequency 165 Hz is sounded, given the speed of sound is 335 m/s?

<p>5 (D)</p> Signup and view all the answers

What will happen to the observed frequency if a source is moving away from a stationary observer at half the velocity of sound?

<p>one-third (C)</p> Signup and view all the answers

Which statement correctly describes how the Doppler effect for light differs from that for sound?

<p>The relative frequency shift is smaller for light than for sound. (A)</p> Signup and view all the answers

An observer moving towards a stationary sound source with a speed one-fifth of the speed of sound hears a frequency $ ext{f}$ from the source. What happens to the observed frequency?

<p>increases (A)</p> Signup and view all the answers

What is the observed frequency of a siren emitting sound at 800 Hz when it moves away at a speed of 30 m/s and the listener is stationary?

<p>770 Hz (B)</p> Signup and view all the answers

What is the maximum frequency shift achievable when a sound source approaches an observer at the speed of sound?

<p>double the original frequency (C)</p> Signup and view all the answers

In what scenario can the speed of sound in air be considered valid when analyzing sound frequency shifts?

<p>Only when temperature is constant (D)</p> Signup and view all the answers

Flashcards

Wave speed of Wave 1

Wave speed is determined by the ratio of angular frequency to wave number. For Wave 1, the wave number and angular frequency are 3 and 6, respectively, yielding a speed of 2 meters per second.

Speed of sound in gases

The speed at which sound waves propagate through a gas, related to the pressure and the density of the gas.

Linear density of a string

The mass per unit length of a string.

Wave speed of Wave 2

Wave speed for Wave 2 is determined by the ratio of the angular frequency to wave number, which are 12 and 4 respectively. Therefore it has a speed of 3 meters per second.

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Wave speed of Wave 3

Wave speed for Wave 3 is determined by the ratio of the angular frequency to wave number, which are 11 and 5 respectively. Thus, the speed is 2.2 meters per second.

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Wave equation of a string

Mathematical representation of the wave's motion on a string. Includes terms for amplitude, wave number, and angular frequency.

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Tension in a string

Force applied along the string that determines how fast the wave travels.

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Maximum transverse string speed (Wave 1)

The maximum speed at which points on the string move perpendicular to the direction of wave propagation. It is the product of angular frequency and amplitude.

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Speed of sound in air

Velocity of sound waves in the air at a given temperature, which factors influence its value.

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Maximum transverse string speed (Wave 2)

The maximum speed of the string’s points when a wave moves across it. It's found by multiplying amplitude and angular frequency

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Intensity level

Measure of the loudness of a sound, in decibels (dB).

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Maximum transverse string speed (Wave 3)

The maximum speed of the string’s points when a wave moves across it. It's found by multiplying amplitude and angular frequency

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Sound waves in moist vs. dry air

Velocity of sound is slightly lower in moist air vs. dry air at the same temperature conditions.

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Wave number

A measure of how many waves fit into a given distance. A higher wave number suggests that more waves will fit into the distance, implying a shorter wavelength.

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Angular frequency

The rate at which the wave oscillates, measured in radians per second.

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Types of waves produced by a motorboat

The waves produced are both transverse and longitudinal, a combination of both.

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Velocity of sound in gas

Depends on the density and elasticity of the gas.

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Sound Intensity change

Sound intensity is proportional to the square of the amplitude and inversely proportional to frequency.

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Sound velocity in water and air

Velocity of sound in water is 1450 m/s, and in air is 330 m/s

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Sound velocity ratio

The ratio of the velocities of sound in two monoatomic gases depends on their densities

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Sound frequency and wavelength change

Frequency remains unchanged when sound moves from one medium to another, but the wavelength changes.

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Amplitude and Energy relations

The energy of a sound wave is proportional to the square of its amplitude and inversely proportional to the frequency.

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Time period and SHM

The time period of Simple Harmonic Motion (SHM) of a particle is 12 seconds.

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Sound amplitude and intensity linked

Sound intensity is related to the square of sound amplitude and the inverse of frequency

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Resonant Frequency

The specific frequency at which a system (like an air column in a pipe) vibrates with maximum amplitude. It's determined by the length of the pipe and the speed of sound.

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Closed Pipe Resonance

A closed pipe (closed at one end) resonates when the length of the pipe is a quarter wavelength (λ/4), three-quarters wavelength (3λ/4), or any odd multiple of a quarter wavelength.

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Wave Equation

A mathematical expression describing the behavior of a wave, typically including terms for amplitude, wavelength, frequency, and time.

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Wave Speed

The rate at which a wave travels through a medium. It's calculated by dividing the angular frequency of the wave by its wave number.

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Tension & Wave Speed

The speed of a wave on a string is directly proportional to the square root of the tension in the string. Higher tension means faster wave speed.

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Resonance frequency (closed pipe)

The frequency at which a closed pipe vibrates most strongly, producing a resonant sound.

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Resonance frequency (open pipe)

The frequency at which an open pipe vibrates most strongly, producing a resonant sound, in which both ends are open.

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Doppler Effect

The apparent change in frequency of a wave (like sound or light) due to the relative motion between the source and the observer.

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Open pipe fundamental frequency

The lowest frequency at which a pipe open at both ends resonates.

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Closed pipe fundamental frequency

The lowest frequency at which a pipe closed at one end resonates.

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Wavelength

The distance between two consecutive crests or troughs of a wave.

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Frequency of Resonance (closed pipe)

The frequency at which the length of the column produces resonance with a tuning fork.

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Beats (acoustics)

The periodic variations in loudness of sound produced by superposition of two waves having slightly different frequencies.

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Doppler effect for sound

The change in frequency of a sound wave due to the relative motion between the source and the observer.

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Doppler effect for light vs sound

The Doppler effect for light differs from sound because light has a constant speed, unlike sound that is dependent on the medium.

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Frequency shift (sound)

The change in the perceived frequency (higher or lower) of a sound as the sound source moves relative to the observer.

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Moving source, stationary observer (sound)

If a sound source moves towards a stationary observer, the observer will hear a higher frequency. If it moves away, a lower frequency.

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Observer moving towards source (sound)

If an observer moves towards a stationary sound source, the observer will hear a higher frequency. The reverse is true if the observer moves away from the source.

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Sound velocity (constant)

Speed of sound is independent of the source's velocity but depends on the transmission medium, pressure, temperature, etc..

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Frequency and wavelength change

Doppler effect changes observed frequency and wavelength.

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Sound beats

Interference pattern produced when sound sources create wave patterns with slightly different frequencies (e.g., the horn of a moving vehicle towards a wall).

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Study Notes

Wave and its Characteristics

  • Water waves can be transverse, longitudinal, or a combination of both.
  • Sound waves are not polarized because they require a medium for propagation and are longitudinal.
  • The time between a lightning flash and the sound of thunder can be used to calculate the distance of the flash. A thunderclap heard 5.5 seconds after a flash means the flash is 1780 meters away.

Progressive Wave

  • The equation Y= 4sin (Ï€/6(tx/8Ï€))x, y are in centimeters. The wavelength is 18 centimeters. Amplitude is 4 cm. Velocity is 20 (cm/s). Frequency is 20Hz.
  • The equation of a progressive wave can be modified with different amplitude and frequency. The equation will be y = 0.5 cos(Ï€t – Ï€x).

Longitudinal and Transverse Waves

  • Transverse waves can only propagate in solids.
  • Transverse waves can propagate in solids but not in gases.
  • Transverse waves are waves that travel perpendicular to the direction of the wave.
  • Longitudinal waves travel parallel to the direction of the wave.

Sound Waves

  • The speed of sound in air is proportional to the square root of the atmospheric pressure.
  • If the frequency of a sound wave is 300 Hz, and if the speed of another wave is 150 Hz, the speed will remain the same.
  • A wave with a frequency of 500Hz travels between points X and Y. The distance between X and Y is 600 m, and the time it takes is 2 s. The number of wavelengths in the distance is 1000.

Reflection of Waves

  • The distance between a man on a cliff and the point where the sound is reflected is 680 meters, given a sound velocity of 340 meters/second.

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