Chapter 7: Q24P (page 345)

The velocity of sound in sea water is about $1530 m / \sec$ . Write an equation for a sinusoidal sound wave in the ocean, of amplitude 1 and frequency $1000 hertz$ .

Short Answer

Expert verified

The equation for a sinusoidal sound wave is $y = \sin 2 000 π (\frac{x}{1530} - t)$ .

Step by step solution

Given data

The dimensions are given as follows:

Amplitude, $A = 1 .$

Frequency, $f = 1000 hertz .$

Velocity, $v = 1530 m / \sec .$

Concept of Sinusoidal sound wave

The trigonometric cosine function can be used to explain a sinusoid's unique functional form, and the most fundamental sinusoid can be written as $A s i n (2 π (f t + ϕ))$

Calculation to find the dimension of the wave equation

Following is a standard wave equation, $y = A \sin (\frac{2 π}{λ} (x - v t))$ .

Time period is the time required to travel a distance of .

So, $(d i s \tan c e) = (s p e e d) (t i m e) .$

$λ = v T$

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

$λ = \frac{v}{f}$

Hence, $v = λ f$ .

Put the value of the obtained dimensions in the sinusoidal wave equation

Now, solve the wave equation as follows:

$y = A \sin (\frac{2 π}{λ} (x - v t)) y = A \sin (\frac{2 π v}{λ} (\frac{x}{v} - t))$

Since, $(v = λ f) .$ .

$y = A \sin (\frac{2 π (λ f)}{λ} (\frac{x}{v} - t)) y = A \sin 2 π f (\frac{x}{v} - t)$

Now, substitute all the value in above equation as follows:

$y = \sin 2 000 π (\frac{x}{1530} - t)$

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The velocity of sound in sea water is about $1530 m / \sec$ . Write an equation for a sinusoidal sound wave in the ocean, of amplitude 1 and frequency $1000 hertz$ .

Short Answer

Step by step solution

Given data

Concept of Sinusoidal sound wave

Calculation to find the dimension of the wave equation

Put the value of the obtained dimensions in the sinusoidal wave equation

One App. One Place for Learning.

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The velocity of sound in sea water is about 1530m/sec. Write an equation for a sinusoidal sound wave in the ocean, of amplitude 1 and frequency1000hertz .

Short Answer

Step by step solution

Given data

Concept of Sinusoidal sound wave

Calculation to find the dimension of the wave equation

Put the value of the obtained dimensions in the sinusoidal wave equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Oscillations

Circular Motion and Gravitation

Conservation of Energy and Momentum

Turning Points in Physics

Scientific Method Physics

Astrophysics

Study anywhere. Anytime. Across all devices.

The velocity of sound in sea water is about $1530 m / \sec$ . Write an equation for a sinusoidal sound wave in the ocean, of amplitude 1 and frequency $1000 hertz$ .