Skip to main content
Ch. 16 - Sound
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 16 - SoundProblema 56a
Capitolo 16, Problema 56a

A source emits sound of wavelengths 2.54 m and 2.72 m in air. How many beats per second will be heard? (Assume T = 20°C.)

Guida verificata passo dopo passo
1
Determine the formula for the frequency of a sound wave: \( f = \frac{v}{\lambda} \), where \( f \) is the frequency, \( v \) is the speed of sound in air, and \( \lambda \) is the wavelength.
At \( T = 20^{\circ}C \), the speed of sound in air is approximately \( v = 343 \, \text{m/s} \). Use this value to calculate the frequencies corresponding to the two given wavelengths: \( \lambda_1 = 2.54 \) m and \( \lambda_2 = 2.72 \) m.
Substitute \( \lambda_1 \) into the formula \( f_1 = \frac{v}{\lambda_1} \) to calculate the first frequency \( f_1 \). Similarly, substitute \( \lambda_2 \) into the formula \( f_2 = \frac{v}{\lambda_2} \) to calculate the second frequency \( f_2 \).
The beat frequency is the absolute difference between the two frequencies: \( f_{\text{beat}} = |f_1 - f_2| \).
Substitute the calculated values of \( f_1 \) and \( f_2 \) into the formula for \( f_{\text{beat}} \) to determine the number of beats per second.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
3m

Concetti chiave

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

Wavelength and Frequency Relationship

The relationship between wavelength and frequency is described by the equation v = fλ, where v is the speed of sound in air, f is the frequency, and λ is the wavelength. As the wavelength increases, the frequency decreases, and vice versa. This concept is crucial for determining the frequencies of the sound waves emitted by the source.
Video consigliato:
Percorso guidato
05:08
Circumference, Period, and Frequency in UCM

Beats Frequency

Beats occur when two sound waves of slightly different frequencies interfere with each other. The beat frequency is calculated as the absolute difference between the two frequencies: f_beat = |f1 - f2|. This concept is essential for solving the problem, as it allows us to find how many beats per second will be heard from the two emitted wavelengths.
Video consigliato:
Percorso guidato
08:46
Beats

Speed of Sound in Air

The speed of sound in air at 20°C is approximately 343 meters per second. This value is important for calculating the frequencies of the sound waves from their respective wavelengths. Knowing the speed of sound allows us to apply the wavelength-frequency relationship to find the frequencies needed to determine the beat frequency.
Video consigliato:
Percorso guidato
05:17
Standing Sound Waves
Pratica correlata
Domanda del libro di testo

Assuming that the maximum displacement of the air molecules in a sound wave is about the same as that of the speaker cone that produces the sound (Fig. 16–46), estimate by how much a loudspeaker cone moves for a fairly loud (105 dB) sound of 35 Hz.

1464
views
Domanda del libro di testo

A guitar string produces 3 beat/s when sounded with a 350-Hz tuning fork and 8 beat/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.

1168
views
Domanda del libro di testo

Expensive amplifier A is rated at 280 W, while the more modest amplifier B is rated at 45 W. What output wattage amp would sound about twice as loud as the 45-W amp?

1556
views