Physics Frequency period

Question

On a keyboard, you strike middle C, whose frequency is 256.0 HzHz. Find the period of one vibration of this tone. As the sound leaves the instrument at a speed of 340 m/sm/s, find its wavelength in air.

Answer 1

To find the period and wavelength of a tone with a frequency of 256.0 Hz, we can use the basic definitions of period and wavelength in the context of wave physics.

1. Period Calculation: The period T of a wave is the reciprocal of its frequency f. The formula to calculate the period is:
2. T=1/f​
3. Plugging in the frequency:
4. T=1/256.0 Hz=0.00390625 seconds
5. So, the period of one vibration of the middle C tone is approximately 0.00391 seconds.
6. Wavelength Calculation: The wavelength λ of a sound wave can be calculated using the formula:
7. λ=v/f​ where v is the speed of sound in air, and f is the frequency of the sound. Given that the speed of sound in air v is approximately 340 m/s:
8. λ=340 m/s/256.0 Hz = 1.328125 meters
9. Therefore, the wavelength of the middle C tone in air is approximately 1.33 meters.

In summary:

1. The period of one vibration of the middle C tone is about 0.00391 seconds.
2. The wavelength of the tone in air is approximately 1.33 meters.

Answer 2

Period T = 1/f = 1/256 s = 0.00391 s; λ = vT = 340m/s·0.00391s = 1.328 m