Chapter 7: Q23P (page 345)

Write an equation for a sinusoidal sound wave of amplitude 1 and frequency 440 hertz ( 1hertz means 1 cycle per second). (Take the velocity of sound to be 350 m/sec).

Short Answer

Expert verified

The equation for a sinusoidal sound wave is, $y = sin 880 π (\frac{x}{350} - t)$ .

Step by step solution

Given data

The dimensions are given as follows:

Amplitude, A = 1 .

Frequency, f = 440hertz.

Velocity, v = 350 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 $A sin (2 π (f t + ϕ))$

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 $λ$ .

So, (distance) = (speed)(time)

$λ = v T$

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:

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

Since,.

role="math" localid="1659247048406" $y = A \sin \frac{2 π (λ f)}{λ} (\frac{x}{v} - t) y = A \sin 2 π v (\frac{x}{v} - t)$ .

Now substitute all the values in the above equation as follows:

$y = sin 880 π (\frac{x}{350} - t)$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Write an equation for a sinusoidal sound wave of amplitude 1 and frequency 440 hertz ( 1hertz means 1 cycle per second). (Take the velocity of sound to be 350 m/sec).

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

Mechanics and Materials

Electrostatics

Modern Physics

Electromagnetism

Physics of Motion

Dynamics

Study anywhere. Anytime. Across all devices.