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Becky and Rajiv are standing at different points in along tunnel while Naomi adjusts her bass amplifier atone end. As Naomi plays an 88 Hz tone, Becky cannothear much and Rajiv complains that the volume is tooloud. What is the minimum distance between Beckyand Rajiv? (Use 343 m/s for the speed of sound.)

Question

Becky and Rajiv are standing at different points in along tunnel while Naomi adjusts her bass amplifier atone end. As Naomi plays an 88 Hz tone, Becky cannothear much and Rajiv complains that the volume is tooloud. What is the minimum distance between Beckyand Rajiv? (Use 343 m/s for the speed of sound.)

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Solution

To solve this problem, we need to understand that Rajiv is hearing a loud sound because he is at a point of constructive interference, where the sound waves are adding up to make a louder sound. This happens at the antinodes of the standing wave in the tunnel. Becky, on the other hand, is hearing a quiet sound because she is at a point of destructive interference, where the sound waves are cancelling each other out. This happens at the nodes of the standing wave.

The distance between two nodes or two antinodes in a standing wave is equal to one wavelength. The distance between a node and an antinode is equal to half a wavelength.

Given that the frequency of the sound is 88 Hz and the speed of sound is 343 m/s, we can use the formula for the speed of a wave (v = fλ) to find the wavelength (λ = v/f).

λ = 343 m/s / 88 Hz = 3.9 m

Since Becky and Rajiv are at a node and an antinode respectively, the minimum distance between them is half a wavelength, which is 3.9 m / 2 = 1.95 m.

This problem has been solved

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