Wave Frequency and Wavelength Calculation

What is the frequency of the motor driving a string with waves of wavelength 0.48 m traveling at 48 m/s?

If the speed of the waves on the string increases to 96 m/s, what happens to the wavelength if the frequency remains constant at 10 Hz?

If the frequency is doubled to 20 Hz, what effect does this have on the wavelength?

What would be the new speed of the waves on the string if the frequency is halved to 5 Hz with a wavelength of 0.48 m?

If the waves have a wavelength of 9.6 m, what is the corresponding frequency when the speed is 48 m/s?

Wave Properties and Relationships

The speed of a wave (v) can be calculated using the formula: v = f × λ, where f is frequency and λ is wavelength.
For a string with a wavelength of 0.48 m traveling at a speed of 48 m/s, the frequency can be determined as follows:
- f = v / λ = 48 m/s / 0.48 m = 100 Hz.

Changes in Speed and Wavelength

If the speed of waves on the string increases to 96 m/s while maintaining a constant frequency of 10 Hz, the wavelength will change because:
- λ = v / f = 96 m/s / 10 Hz = 9.6 m.

Effects of Doubling Frequency

Doubling the frequency from 10 Hz to 20 Hz results in a decrease in wavelength while speed remains constant:
- If the speed is still 96 m/s, then λ = v / f = 96 m/s / 20 Hz = 4.8 m.

Speed Changes with Frequency Adjustment

Halving the frequency from 10 Hz to 5 Hz while maintaining a wavelength of 0.48 m requires recalculating the new speed:
- Using the formula v = f × λ = 5 Hz × 0.48 m = 2.4 m/s.

Frequency Calculation with Given Wavelength

For waves with a wavelength of 9.6 m and a speed of 48 m/s, the corresponding frequency can be calculated:
- f = v / λ = 48 m/s / 9.6 m = 5 Hz.

Test your understanding of wave properties by calculating the wavelength of waves on a string with a given frequency and speed. Choose the correct answer from the options provided.