AP Physics 1 Exam Question

A speaker emits a sound wave with a frequency of 500 Hz. The sound wave travels through air at a speed of 343 m/s.

a) Calculate the wavelength of this sound wave.

b) Another sound wave with a frequency of 1000 Hz and a wavelength of 0.171 m is emitted. Calculate the speed of this sound wave.

c) State whether the speed of sound wave in air depends on its frequency or not, and explain your answer.

Answer

a) The relationship between the speed of a wave (v), its frequency (f), and its wavelength (λ) is given by the formula v = f * λ.

Given: Frequency (f) = 500 Hz Speed (v) = 343 m/s

Rearranging the formula, we have: λ = v / f

Plugging in the values, we get: λ = 343 m/s / 500 Hz

Calculating the wavelength, we get: λ = 0.686 m

Therefore, the wavelength of the sound wave is 0.686 m.

b) We can use the same formula, v = f * λ, to calculate the speed of the sound wave.

Given: Frequency (f) = 1000 Hz Wavelength (λ) = 0.171 m

Rearranging the formula, we have: v = f * λ

Plugging in the values, we get: v = 1000 Hz * 0.171 m

Calculating the speed, we get: v = 171 m/s

Therefore, the speed of the sound wave is 171 m/s.

c) No, the speed of a sound wave in air does not depend on its frequency. The speed of sound in a given medium is determined by the properties of that medium, such as its density and elasticity. In air, the speed of sound is approximately 343 m/s at room temperature. The frequency of a sound wave only affects its wavelength, with higher frequencies having shorter wavelengths and lower frequencies having longer wavelengths.