Wave Model Terms and Wave Motion Principles

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Questions and Answers

Consider two waves traveling in the same medium. How does a change in wavelength of one wave affect its speed, assuming the medium remains constant?

Both waves will have the same speed regardless of their wavelengths. (correct)

The speed of the waves will vary non-linearly with the inverse square of the wavelength.

The wave with a longer wavelength will travel faster.

The wave with a shorter wavelength will travel faster.

A wave transitions from air into water. Which property of the wave remains unchanged during the transition?

Amplitude

Wavelength

Speed

Frequency (correct)

What is the relationship between the frequency ($f$) and the period ($T$) of a wave?

$f = \sqrt{T}$

$f = T$

$f = T^2$

$f = 1/T$ (correct)

Given a wave with a frequency of 5 Hz and a wavelength of 2 meters, what is the speed of the wave?

10 m/s (D) Signup and view all the answers

Which part of a transverse wave is characterized as the lowest point below its equilibrium position?

Trough (C) Signup and view all the answers

How is the wavelength ($\lambda$) defined in the context of a wave?

The distance between two consecutive crests or troughs. (C) Signup and view all the answers

If the frequency of a wave is doubled while it travels through the same medium, what happens to its wavelength?

The wavelength is halved. (D) Signup and view all the answers

Consider two waves, Wave A and Wave B, traveling through different media. Wave A has a higher speed than Wave B. Which of the following conclusions can be accurately drawn?

The medium through which Wave A travels offers less resistance to wave propagation than the medium through which Wave B travels. (C) Signup and view all the answers

How does increasing the frequency of a wave affect its properties upon entering a different medium, assuming the wave speed remains constant?

The wavelength decreases proportionally to the frequency increase. (D) Signup and view all the answers

If the amplitude of a wave is doubled and the frequency is halved, what is the resulting change in the wave's intensity?

The intensity remains the same. (C) Signup and view all the answers

A sound wave traveling through air has a period of 400 microseconds. What is the frequency of this wave?

2.5 kHz (B) Signup and view all the answers

What occurs when a transverse wave traveling in a denser medium is incident on a rarer medium?

It is reflected without any change in phase. (D) Signup and view all the answers

Given that the intensity of a wave is directly proportional to the square of its amplitude and frequency, how would you explain the relationship mathematically if 'k' is the proportionality constant?

$I = k A^2 f^2$ (D) Signup and view all the answers

Consider two waves with amplitudes A1 and A2. What condition must be met for their superposition to result in complete destructive interference at a point?

A1 must be equal to A2 and they must be out of phase by $\pi$ radians. (D) Signup and view all the answers

A transverse wave is reflected from a boundary. Under what conditions would the reflected wave undergo a phase shift of $\pi$ radians?

When the wave travels from a rarer medium to a denser medium. (D) Signup and view all the answers

If a wave's frequency is tripled while its speed remains constant, what happens to its period?

The period is divided by three. (C) Signup and view all the answers

A string with a linear mass density of $5.00 \times 10^{-3}$ kg/m is under a tension of 80.0 N. What is the speed of the wave produced in the string?

40 m/s (C) Signup and view all the answers

A stretched steel wire is 1 m long and has a fundamental frequency of 250 Hz. What is the velocity of the transverse wave in it?

500 m/s (A) Signup and view all the answers

How is the number of antinodes (N) related to the harmonic number (H) for standing waves?

$N = H + 1$ (D) Signup and view all the answers

What distinguishes the fundamental frequency from overtones in the context of waves?

The fundamental frequency is the lowest frequency produced, while overtones are higher frequencies. (A) Signup and view all the answers

A guitar string is vibrating at its third harmonic. If the length of the string is $L$, what is the distance between two consecutive nodes?

$L/3$ (A) Signup and view all the answers

Consider two strings of identical length and tension. String A has a linear mass density twice that of String B. What is the ratio of the fundamental frequency of String A to that of String B?

$1/\sqrt{2}$ (C) Signup and view all the answers

A string fixed at both ends vibrates in its fifth harmonic. At what points along the string (excluding the endpoints) can you touch the string without disturbing the standing wave?

At points $L/5$, $2L/5$, $3L/5$, and $4L/5$ from one end, where $L$ is the length of the string. (D) Signup and view all the answers

A standing wave is formed on a string of length $L$ fixed at both ends. If the frequency of the wave is doubled, which of the following is true about the new standing wave pattern?

The number of antinodes is approximately doubled. (B) Signup and view all the answers

In the context of sound wave interference, what condition primarily dictates whether the interference will be constructive or destructive?

The relative phase of the waves at the point of interaction; in-phase waves lead to constructive interference, while those out-of-phase lead to destructive interference. (D) Signup and view all the answers

What is the primary requirement for sound sources to be considered coherent in the context of interference?

They must emit sound waves with identical and constant phase relationship. (C) Signup and view all the answers

How does the path difference between two sound waves relate to the type of interference that occurs?

A path difference equal to an integer multiple of the wavelength leads to constructive interference, while a path difference equal to an odd multiple of half the wavelength leads to destructive interference. (B) Signup and view all the answers

In what scenario does a 'silence zone' typically occur in the context of sound wave interference?

A silence zone arises in areas where sound waves from multiple sources destructively interfere, resulting in minimal sound intensity. (C) Signup and view all the answers

What is the effect of destructive interference on the loudness and intensity of sound?

Both the loudness and intensity of sound decrease due to the cancellation of waves. (B) Signup and view all the answers

What occurs when the compression of one sound wave aligns with the rarefaction of another wave at a specific point?

Destructive interference, leading to a reduced sound intensity at that point. (B) Signup and view all the answers

Why is it essential for sound waves to travel in the same medium to observe interference effects?

Different media can cause variations in wave speed and wavelength, disrupting the phase relationship needed for stable interference patterns. (B) Signup and view all the answers

In the context of constructive sound interference, how does the resulting sound differ from the individual sounds that interfere?

The resulting sound is louder, due to the increased amplitude from the reinforcement of the waves. (D) Signup and view all the answers

Under what conditions does constructive interference of sound waves predominantly occur?

When two identical waves meet at a point in phase, reinforcing each other to produce a larger amplitude. (C) Signup and view all the answers

What is the fundamental principle that governs the superposition of waves in a medium?

The total displacement at any point is the algebraic sum of the displacements of all individual waves. (D) Signup and view all the answers

Consider $n$ waves acting simultaneously on a particle in a medium. If the displacement due to each wave is given by $y_i$, where $i$ ranges from 1 to $n$, what is the resultant displacement $Y$ of the particle?

$Y = y_1 + y_2 + ... + y_n$ (C) Signup and view all the answers

Two identical sound waves are propagating in the same direction through a medium. What phenomenon occurs when these waves 'mix up' or combine?

Interference, resulting in the superposition of the waves. (D) Signup and view all the answers

What happens to the energy of two waves that interfere destructively?

The energy is redistributed in space, with some areas having increased energy and others decreased. (C) Signup and view all the answers

How does the principle of superposition apply when analyzing complex soundscapes, such as in an orchestra?

It enables the prediction of the combined sound wave by summing the individual sound waves, accounting for phase and amplitude. (C) Signup and view all the answers

In the context of sound interference, what distinguishes 'identical' waves from similar waves with slightly different characteristics?

Identical waves have the same frequency, amplitude, and phase relationship, whereas similar waves may differ in these properties. (D) Signup and view all the answers

If two identical sound waves with amplitudes $A_1$ and $A_2$ interfere constructively at a point, and $A_1 = A_2 = A$, what is the amplitude of the resulting wave at that point?

$2A$ (C) Signup and view all the answers

Two identical sound waves, each with amplitude $A$, interfere in a medium. Under what conditions regarding their phase difference ($\phi$) will the resulting wave have an amplitude of $\frac{A}{2}$?

$\phi = \arccos(\frac{3}{4})$ (A) Signup and view all the answers

Consider two sound waves with amplitudes $A_1$ and $A_2$ interfering destructively. If the resulting amplitude is zero, what can be definitively concluded about the relationship between the initial waves at the point of interference?

The waves have a phase difference of $\pi$ radians and $A_1 = A_2$. (C) Signup and view all the answers

A string is fixed at both ends and supports a standing wave with three nodes (including the endpoints). If the length of the string is $L$, what is the wavelength of the standing wave?

$L$ (D) Signup and view all the answers

A pipe, open at both ends, has a fundamental frequency $f$. If one end of the pipe is closed, what is the new fundamental frequency, assuming the speed of sound remains constant?

$\frac{1}{2}f$ (A) Signup and view all the answers

The velocity of sound in air at a certain temperature is $v$. If the absolute temperature is doubled and the molar mass of the gas is quadrupled, what is the new velocity of sound?

$\frac{v}{\sqrt{2}}$ (A) Signup and view all the answers

Two speakers emit sound waves of the same frequency and amplitude. At a certain point, the sound intensity is four times what it would be from a single speaker alone. What is the phase difference between the waves at this point?

$0$ radians (A) Signup and view all the answers

A stationary wave is formed by the superposition of two waves, $y_1 = A\sin(kx - \omega t)$ and $y_2 = A\sin(kx + \omega t)$. What is the distance between two consecutive nodes in the resulting wave?

$\frac{\lambda}{2}$ (B) Signup and view all the answers

Consider a scenario where two identical sound sources are emitting waves in phase. At a certain point, the path difference to the listener is $\lambda/2$, where $\lambda$ is the wavelength. If the amplitude of each wave is $A$, what is the resulting amplitude at the listener's location?

$0$ (D) Signup and view all the answers

Flashcards

Constructive Interference

When two waves meet in phase, amplifying sound and increasing loudness.

Destructive Interference

When two waves meet out of phase, canceling each other, reducing sound intensity.