Chapter 7: Q7-13-12MP (page 388)

What would be the apparent frequency of a sound wave represented by
_{$p (t) = \sum_{n = 1}^{\infty} \frac{c o s 60 n π t}{100 {(n - 3)}^{2} + 1} ?$}

Short Answer

Expert verified

The apparent frequency of a sound waveis 90Hz.

Step by step solution

Given Information.

The given equation is $p (t) = \sum_{n = 1}^{\infty} \frac{\cos 60 n π t}{100 {(n - 3)}^{2} + 1} ?$

Step 2: Meaning of the apparent frequency of a sound wave.

When the source moves with velocity towards the stationary listener, the perceived frequency of sound heard by the listener is ten percent higher than the actual frequency of the note emitted by the source.

Find the apparent frequency of a sound wave.

The function $a_{n} = n$ then the function has a sharp spike at n=3

withrole="math" localid="1664373395549" $a_{3} = 1$ , and the next largest terms are:

$a_{2} = a_{4} = \frac{1}{101}$

Hence, they are negligible.

Thus, the apparent frequency is

$180 πt = \frac{2 πt}{T} T = \frac{1}{90}$

Since $T = \frac{1}{f}$

Therefore, the apparent frequency of a sound waveis 90Hz .

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What would be the apparent frequency of a sound wave represented by
_{$p (t) = \sum_{n = 1}^{\infty} \frac{c o s 60 n π t}{100 {(n - 3)}^{2} + 1} ?$}

Short Answer

Step by step solution

Given Information.

Step 2: Meaning of the apparent frequency of a sound wave.

Find the apparent frequency of a sound wave.

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What would be the apparent frequency of a sound wave represented byp(t)=∑n=1∞cos60nπt100(n-3)2+1?

Short Answer

Step by step solution

Given Information.

Step 2: Meaning of the apparent frequency of a sound wave.

Find the apparent frequency of a sound wave.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Wave Optics

Nuclear Physics

Conservation of Energy and Momentum

Fields in Physics

Space Physics

Geometrical and Physical Optics

Study anywhere. Anytime. Across all devices.

What would be the apparent frequency of a sound wave represented by
_{$p (t) = \sum_{n = 1}^{\infty} \frac{c o s 60 n π t}{100 {(n - 3)}^{2} + 1} ?$}