AP Physics 1 Exam Question:

A speaker emitting a sinusoidal sound wave is placed in front of a reflecting wall. The speaker emits sound at a frequency of 800 Hz. The speed of sound in air is approximately 343 m/s.

(a) What is the wavelength of the sound wave emitted by the speaker? (b) If the distance between the speaker and the reflecting wall is 10 meters, determine the distance traveled by the sound wave before it is reflected off the wall. (c) If the sound wave is reflected off the wall and returns to the speaker, what is the total distance traveled by the sound wave?

Answer:

(a) The speed of sound (v) is given as 343 m/s and the frequency (f) of the sound wave emitted by the speaker is 800 Hz.

The formula relating the speed of sound, frequency, and wavelength is:

   v = f * λ

Where: v = speed of sound (m/s) f = frequency of sound wave (Hz) λ = wavelength of the sound wave (m)

Rearranging the formula, we find:

   λ = v / f

Substituting the given values, we get:

   λ = 343 m/s / 800 Hz

Simplifying,

   λ ≈ 0.42875 m

Therefore, the wavelength of the sound wave emitted by the speaker is approximately 0.42875 meters.

(b) The distance between the speaker and the reflecting wall is given as 10 meters.

A sound wave travels twice the distance between the speaker and the reflecting wall before being reflected. This is because the wave travels from the speaker to the wall, reflects off the wall, and then travels back to the speaker.

Therefore, the distance traveled by the sound wave before it is reflected off the wall is:

   2 * 10 meters = 20 meters

Thus, the distance traveled by the sound wave before it is reflected off the wall is 20 meters.

(c) After the sound wave is reflected off the wall, it travels back to the speaker. So the total distance traveled by the sound wave is the sum of the distance traveled to the wall and the distance traveled back to the speaker.

Total distance traveled by the sound wave = Distance to the wall + Distance back to the speaker = 10 meters + 10 meters = 20 meters.

Hence, the total distance traveled by the sound wave is 20 meters.