Math / Algebra

QuestionDoppler Effect - The whistle of a train emits a frequency of 440 Hz. - As it recedes from a stationary receiver at 30 $\mathrm{m} / \mathrm{s}$ , what frequency does the observer hear?

Studdy Solution

STEP 1

1. The source of the sound (train whistle) emits a frequency of 440 Hz.
2. The train is moving away from the observer at a speed of 30 m/s.
3. The speed of sound in air is approximately 343 m/s (assuming standard conditions).
4. We are using the Doppler effect formula for sound to find the observed frequency.

STEP 2

1. Understand the Doppler effect formula for sound.
2. Identify the known values and variables.
3. Substitute the known values into the Doppler effect formula.
4. Solve for the observed frequency.

STEP 3

Understand the Doppler effect formula for sound.
The Doppler effect formula for sound when the source is moving away from the observer is:
$f' = \frac{f \cdot v}{v + v_s}$
where: - $f'$ is the observed frequency. - $f$ is the emitted frequency (440 Hz). - $v$ is the speed of sound in air (343 m/s). - $v_s$ is the speed of the source (30 m/s).

STEP 4

Identify the known values and variables.
- Emitted frequency, $f = 440 \, \text{Hz}$ - Speed of sound, $v = 343 \, \text{m/s}$ - Speed of the source, $v_s = 30 \, \text{m/s}$

STEP 5

Substitute the known values into the Doppler effect formula.
$f' = \frac{440 \cdot 343}{343 + 30}$

STEP 6

Solve for the observed frequency.
Calculate the denominator:
$343 + 30 = 373$
Substitute back into the equation:
$f' = \frac{440 \cdot 343}{373}$
Calculate the observed frequency:
$f' \approx \frac{151,120}{373} \approx 405.66 \, \text{Hz}$
The frequency observed by the stationary receiver is approximately:
$\boxed{405.66 \, \text{Hz}}$

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QuestionDoppler Effect - The whistle of a train emits a frequency of 440 Hz. - As it recedes from a stationary receiver at 30 $\mathrm{m} / \mathrm{s}$ , what frequency does the observer hear?

Studdy Solution

STEP 1

STEP 2

1. Understand the Doppler effect formula for sound.
2. Identify the known values and variables.
3. Substitute the known values into the Doppler effect formula.
4. Solve for the observed frequency.

STEP 3

STEP 4

Identify the known values and variables.
- Emitted frequency, $f = 440 \, \text{Hz}$ - Speed of sound, $v = 343 \, \text{m/s}$ - Speed of the source, $v_s = 30 \, \text{m/s}$

STEP 5

Substitute the known values into the Doppler effect formula.
$f' = \frac{440 \cdot 343}{343 + 30}$

STEP 6

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QuestionDoppler Effect - The whistle of a train emits a frequency of 440 Hz. - As it recedes from a stationary receiver at 30 m/s\mathrm{m} / \mathrm{s}m/s, what frequency does the observer hear?

Studdy Solution

STEP 1

STEP 2

1. Understand the Doppler effect formula for sound.2. Identify the known values and variables.3. Substitute the known values into the Doppler effect formula.4. Solve for the observed frequency.

STEP 3

STEP 4

Identify the known values and variables.- Emitted frequency, f=440 Hz f = 440 \, \text{Hz} f=440Hz - Speed of sound, v=343 m/s v = 343 \, \text{m/s} v=343m/s - Speed of the source, vs=30 m/s v_s = 30 \, \text{m/s} vs​=30m/s

STEP 5

Substitute the known values into the Doppler effect formula.f′=440⋅343343+30 f' = \frac{440 \cdot 343}{343 + 30} f′=343+30440⋅343​

STEP 6

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QuestionDoppler Effect - The whistle of a train emits a frequency of 440 Hz. - As it recedes from a stationary receiver at 30 $\mathrm{m} / \mathrm{s}$ , what frequency does the observer hear?

1. Understand the Doppler effect formula for sound.
2. Identify the known values and variables.
3. Substitute the known values into the Doppler effect formula.
4. Solve for the observed frequency.

Identify the known values and variables.
- Emitted frequency, $f = 440 \, \text{Hz}$ - Speed of sound, $v = 343 \, \text{m/s}$ - Speed of the source, $v_s = 30 \, \text{m/s}$

Substitute the known values into the Doppler effect formula.
$f' = \frac{440 \cdot 343}{343 + 30}$