A sound wave with a frequency of 400.0 Hz is incident upon a set of stairs. The reflected waves from the vertical surfaces of adjacent steps interfere destructively. What is the minimum tread depth of a step for this to occur?

Jacoby Erickson

Jacoby Erickson

Answered question

2022-10-15

A sound wave with a frequency of 400.0 Hz is incident upon a set of stairs.
The reflected waves from the vertical surfaces of adjacent steps interfere destructively. What is the minimum tread depth of a step for this to occur?

Answer & Explanation

bargeolonakc

bargeolonakc

Beginner2022-10-16Added 16 answers

Given
The frequency of the sound wave is ν = 400 H z
Required:
Finding the minimum tread depth of a step.
Calculation:
In order to evaluate the wave's speed, we Use the following relation:
v = ν λ
Divide both sides by ν , then we get
λ = v ν
d m i n = λ 4
= v 4 ν
= 343 m / s 4 × 400 H z
=0.214m
Result:
d m i n = 0.214 m

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