/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 8 When a particular wire is vibrat... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

When a particular wire is vibrating with a frequency of \(4.00 \mathrm{Hz},\) a transverse wave of wavelength \(60.0 \mathrm{cm}\) is produced. Determine the speed of waves along the wire.

Short Answer

Expert verified
The speed of the waves along the wire is \(2.4 m/s\).

Step by step solution

01

Convert units

First, convert the wavelength from centimeters to meters to match with the standard SI unit. The conversion rate is 1 meter = 100 centimeters. So, \(60.0 cm = 60.0/100 = 0.6 m\).
02

Use the formula

Next, insert the frequency and the converted wavelength into the formula to find the speed of the wave as follows: Speed = Frequency x Wavelength = \(4.00 Hz x 0.6 m = 2.4 m/s\).
03

Interpret the Results

The calculated speed of the waves along the wire comes out to be \(2.4 m/s\). This means that a wave travels a distance of 2.4 meters along the wire in one second.

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.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Wave Frequency
Wave frequency is a fundamental concept when dealing with waves, whether they are on a string or light. It denotes the number of wave cycles that pass a particular point in a specific timeframe, typically one second. This is why frequency is measured in hertz (Hz), where one hertz represents one cycle per second.

For instance, in our exercise, the frequency of the wave is given as 4 Hz. This means 4 complete waves flow past a point each second. Understanding wave frequency is crucial because it ties directly into calculating wave speed when combined with the wavelength, which we will discuss shortly. High frequencies imply more cycles per second, while lower frequencies mean fewer cycles per second.
  • Frequency is a key attribute along with wavelength and speed.
  • Measured in hertz (Hz) - 1 Hz means 1 cycle/second.
  • Helps in determining the wave speed when used with wavelength.
Wavelength Conversion
Converting wavelength to the correct units is essential, especially when dealing with calculations related to wave speed. Often problems present wavelengths in centimeters; however, the standard SI unit for length is meters. Hence, you need to convert these measurements for consistency in your calculations.

In our example, the wavelength is provided as 60.0 cm. To convert to meters, divide by 100 (since 1 meter = 100 centimeters). This results in a wavelength of 0.6 meters. This conversion is crucial and cannot be overlooked, as using inconsistent units can lead to incorrect calculations and misunderstandings of wave phenomena.
  • Wavelength must be in meters to apply wave speed formulas accurately.
  • Convert from cm to m: divide by 100.
  • In our case, 60.0 cm converts to 0.6 m.
SI Units
The International System of Units (SI) is the world's most widely used system of measurement, ensuring consistency and clarity in scientific communication. Using SI units allows scientists from different regions or paradigms to exchange, compare, and analyze information seamlessly.

In physics, when dealing with waves, speed is generally measured in meters per second (m/s), frequency in hertz (Hz), and wavelength in meters (m). Adhering to SI units eliminates confusion and errors which might arise from converting or miscalculating data presented in different units of measurement.

In the exercise example, the frequency is already in hertz, but the wavelength needed conversion from centimeters to meters to use the wave speed formula effectively. This conversion ensures that when multiplying frequency and wavelength, the units are compatible, resulting in the correct measurement of speed in meters per second.
  • SI Units ensure standardization and consistency globally.
  • Primary SI units for waves: Speed (m/s), Wavelength (m), Frequency (Hz).
  • Accurate calculations hinge on consistent unit use.

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

S and P waves, simultaneously radiated from the hypocenter of an earthquake, are received at a seismographic station \(17.3 \mathrm{s}\) apart. Assume the waves have traveled over the same path at speeds of \(4.50 \mathrm{km} / \mathrm{s}\) and \(7.80 \mathrm{km} / \mathrm{s} .\) Find the distance from the seismograph to the hypocenter of the quake.

A transverse sinusoidal wave on a string has a period \(T=25.0 \mathrm{ms}\) and travels in the negative \(x\) direction with a speed of \(30.0 \mathrm{m} / \mathrm{s} .\) At \(t=0,\) a particle on the string at \(x=0\) has a transverse position of \(2.00 \mathrm{cm}\) and is traveling downward with a speed of \(2.00 \mathrm{m} / \mathrm{s} .\) (a) What is the amplitude of the wave? (b) What is the initial phase angle? (c) What is the maximum transverse speed of the string? (d) Write the wave function for the wave.

A two-dimensional water wave spreads in circular ripples. Show that the amplitude \(A\) at a distance \(r\) from the initial disturbance is proportional to \(1 / \sqrt{r}\). (Suggestion: Consider the energy carried by one outward- moving ripple.)

A \(2.00-\mathrm{kg}\) block hangs from a rubber cord, being supported so that the cord is not stretched. The unstretched length of the cord is \(0.500 \mathrm{m},\) and its mass is 5.00 g. The "spring constant" for the cord is \(100 \mathrm{N} / \mathrm{m} .\) The block is released and stops at the lowest point. (a) Determine the tension in the cord when the block is at this lowest point. (b) What is the length of the cord in this "stretched" position? (c) Find the speed of a transverse wave in the cord if the block is held in this lowest position.

A traveling wave propagates according to the expression \(y=(4.0 \mathrm{cm}) \sin (2.0 x-3.0 t),\) where \(x\) is in centimeters and \(t\) is in seconds. Determine (a) the amplitude, (b) the wavelength, (c) the frequency, (d) the period, and (e) the direction of travel of the wave.

See all solutions

Recommended explanations on Physics Textbooks

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.