Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 18: Problem 4

Write an expression describing a transverse wave traveling along a string in the \(+x\) direction with wavelength \(11.4 \mathrm{~cm}\), frequency \(385 \mathrm{~Hz}\), and amplitude \(2.13 \mathrm{~cm} .\)

Short Answer

Expert verified
The expression for the wave is y(x, t) = 0.0213*sin(55.02x - 2419.47t).

Step by step solution

01

Calculate the wave number (k)

The wave number is calculated using the formula k = 2π/λ. The given wavelength λ equals 11.4 cm or 0.114 m. Substituting this into the formula gives k = 2π/0.114 ≈ 55.02 rad/m.
02

Calculate the angular frequency (w)

The angular frequency is calculated by the formula w = 2πf. The given frequency f is 385 Hz. Substituting this into the formula leads to w = 2π*385 ≈ 2419.47 rad/s.
03

Write the wave equation

After calculating the wave number and angular frequency, we can write our wave equation. In this question, the given amplitude A is 2.13 cm or 0.0213 m. Now we substitute w, k, and A into the wave equation y = A*sin(kx - wt + φ). By doing the substitution, the equation becomes:y(x, t) = 0.0213*sin(55.02x - 2419.47t).

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!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Calculate the speed of a transverse wave in a string of length 2.15 m and mass \(62.5 \mathrm{~g}\) under a tension of \(487 \mathrm{~N}\).

A string \(2.72 \mathrm{~m}\) long has a mass of \(263 \mathrm{~g}\). The tension in the string is \(36.1 \mathrm{~N}\). What must be the frequency of traveling waves of amplitude \(7.70 \mathrm{~mm}\) in order that the average transmitted power be \(85.5 \mathrm{~W}\) ?

An observer measures an intensity of \(1.13 \mathrm{~W} / \mathrm{m}^{2}\) at an unknown distance from a source of spherical waves whose power output is also unknown. The observer walks \(5.30 \mathrm{~m}\) closer to the source and measures an intensity of \(2.41 \mathrm{~W} / \mathrm{m}^{2}\) at this new location. Calculate the power output of the source.

Vibrations from a \(622-\mathrm{Hz}\) tuning fork set up standing waves in a string clamped at both ends. The wave speed for the string is \(388 \mathrm{~m} / \mathrm{s}\). The standing wave has four loops and an amplitude of \(1.90 \mathrm{~mm} .\) (a) What is the length of the string? (b) Write an equation for the displacement of the string as a function of position and time.

The equation of a transverse wave traveling along a string is given by $$ y=(2.30 \mathrm{~mm}) \sin [(1822 \mathrm{rad} / \mathrm{m}) x-(588 \mathrm{rad} / \mathrm{s}) t] $$ Find \((a)\) the amplitude, \((b)\) the frequency, \((c)\) the velocity, \((d)\) the wavelength of the wave, and ( \(e\) ) the maximum transverse speed of a particle in the string.
See all solutions

Recommended explanations on Physics Textbooks

Solid State Physics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Electromagnetism

Read Explanation

Physical Quantities And Units

Read Explanation

Particle Model of Matter

Read Explanation

Measurements

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free