Skip to main content
Ch 16: Traveling Waves
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 16: Traveling WavesProblema 17a
Capitolo 16, Problema 17a

What is the frequency of an electromagnetic wave that has the same wavelength as a 2.5 kHz sound wave in water?

Guida verificata passo dopo passo
1
Step 1: Understand the problem. The goal is to find the frequency of an electromagnetic wave that has the same wavelength as a sound wave in water. The relationship between wavelength, frequency, and speed is given by the formula: v = fλ, where v is the speed, f is the frequency, and λ is the wavelength.
Step 2: Calculate the wavelength of the sound wave in water. Use the formula λ = v/f, where the speed of sound in water is approximately 1500 m/s and the frequency of the sound wave is 2.5 kHz (or 2500 Hz). Substitute these values into the formula to find the wavelength.
Step 3: Recognize that the electromagnetic wave has the same wavelength as the sound wave. The speed of electromagnetic waves in a vacuum (and approximately in air) is the speed of light, c = 3.0 × 108 m/s. Use the formula f = c/λ to calculate the frequency of the electromagnetic wave.
Step 4: Substitute the wavelength calculated in Step 2 into the formula for the electromagnetic wave frequency. Use f = c/λ, where c is the speed of light and λ is the wavelength.
Step 5: Simplify the expression to find the frequency of the electromagnetic wave. Ensure units are consistent throughout the calculation (e.g., meters for wavelength and seconds for time). The result will give the frequency of the electromagnetic wave in Hz.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Electromagnetic Waves

Electromagnetic waves are oscillations of electric and magnetic fields that propagate through space. They travel at the speed of light in a vacuum and encompass a wide range of frequencies and wavelengths, including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. The relationship between frequency and wavelength is fundamental to understanding their behavior.
Video consigliato:
Percorso guidato
05:22
Introduction to Electromagnetic (EM) Waves

Wave Equation

The wave equation relates the speed of a wave to its frequency and wavelength, expressed as v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength. This equation is crucial for calculating the frequency of an electromagnetic wave when its wavelength is known. For electromagnetic waves in a vacuum, the speed is approximately 3 x 10^8 m/s.
Video consigliato:
Percorso guidato
06:28
Equations for Transverse Standing Waves

Sound Waves in Water

Sound waves are mechanical waves that require a medium to travel, such as air, water, or solids. In water, sound travels faster than in air due to the higher density and elasticity of the medium. The frequency of a sound wave, such as the 2.5 kHz mentioned, is related to its wavelength and speed in water, which is essential for comparing it to the frequency of an electromagnetic wave with the same wavelength.
Video consigliato:
Percorso guidato
05:17
Standing Sound Waves
Pratica correlata
Domanda del libro di testo
Show that the displacement D(x,t) = ln(ax + bt), where a and b are constants, is a solution to the wave equation. Then find an expression in terms of a and b for the wave speed.
1682
views
Domanda del libro di testo

A hammer taps on the end of a 4.00-m-long metal bar at room temperature. A microphone at the other end of the bar picks up two pulses of sound, one that travels through the metal and one that travels through the air. The pulses are separated in time by 9.00 ms. What is the speed of sound in this metal?

1796
views
Domanda del libro di testo

What is the speed of sound in air (a) on a cold winter day in Minnesota when the temperature is -25°F, and (b) on a hot summer day in Death Valley when the temperature is 125°F?

1277
views
Domanda del libro di testo

FIGURE EX16.8 is a picture at t = 0 s of the particles in a medium as a longitudinal wave is passing through. The equilibrium spacing between the particles is 1.0 cm. Draw the snapshot graph D(x, t = 0 s) of this wave at t = 0 s.

2055
views
Domanda del libro di testo

A 15-cm-long aluminum tank is filled with ethyl alcohol. A high-frequency ultrasound wave travels horizontally through one wall of the tank and then through the alcohol. There are 275 times more cycles of the wave in the alcohol than in the aluminum wall. How thick is the wall of the tank?

190
views
Domanda del libro di testo

Show that the displacement D(x,t) = cx² + dt², where c and d are constants, is a solution to the wave equation. Then find an expression in terms of c and d for the wave speed.

1837
views