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

Knight Calc 5th Edition

Ch 16: Traveling Waves

Problema 71

Capitolo 16, Problema 71

A battery-powered siren emits 0.50 W of sound power at 1000 Hz. It is dropped from 100 m directly over your head on a 20°C day. 4.0 s after it is released, what are (a) the frequency and (b) the sound intensity level you hear?

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Determine the speed of sound in air at 20°C using the formula:

v = 331 + 0.6 T

, where

T

is the temperature in Celsius. Substitute

T = 20

to find the speed of sound.

Calculate the distance the siren has fallen after 4.0 s using the kinematic equation:

y = h - \frac{1}{2} g t ²

, where

h

is the initial height (100 m),

g

is the acceleration due to gravity (9.8 m/s²), and

t

is the time (4.0 s).

Determine the relative velocity of the siren with respect to the observer using the formula:

v = g t

, where

g

is the acceleration due to gravity and

t

is the time (4.0 s).

Apply the Doppler effect formula to calculate the observed frequency:

f' = f \frac{v}{+}

_ov-v_s, where

f

is the source frequency (1000 Hz),

v

is the speed of sound,

v

_o is the observer's velocity (0 m/s), and

v

_s is the source velocity (calculated in step 3).

Calculate the sound intensity level using the formula:

β = 10 \log (\frac{I}{I}

_o), where

I

is the intensity of the sound at the observer's location and

I

_o is the reference intensity (

1 x 10 - 12

W/m²). To find

I

, use the formula:

I = \frac{P}{4}

, where

P

is the power of the source (0.50 W) and

r

is the distance from the source to the observer (calculated in step 2).

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Doppler Effect

The Doppler Effect describes the change in frequency or wavelength of a wave in relation to an observer moving relative to the wave source. In this scenario, as the siren falls, the frequency of the sound waves it emits will appear to change due to its motion towards the observer, affecting the perceived pitch of the sound.

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Percorso guidato

07:40

The Doppler Effect

Sound Intensity and Intensity Level

Sound intensity is the power per unit area carried by a sound wave, typically measured in watts per square meter (W/m²). The sound intensity level, measured in decibels (dB), quantifies how loud a sound is perceived, using a logarithmic scale relative to a reference intensity. This concept is crucial for determining how the sound from the siren is perceived at a distance.

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Percorso guidato

04:25

Sound Intensity Level and the Decibel Scale

Free Fall Motion

Free fall motion refers to the motion of an object under the influence of gravity alone, without any air resistance. In this case, the siren is dropped from a height of 100 m, and understanding its acceleration due to gravity (approximately 9.81 m/s²) is essential for calculating the time it takes to reach the observer and the changes in sound frequency and intensity during its fall.

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Percorso guidato

08:36

Vertical Motion & Free Fall

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