The frequency of echo will be _______ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of 36 km/h towards a hill from which an echo is heard by the train driver. Velocity of sound in air is 330 m/s.
Correct Answer: 340
Approach Solution - 1
To solve this problem, we apply the Doppler effect formula for sound, which relates the observed frequency to the source frequency, taking into account the velocities of the source, observer, and the medium.
First, we convert the train's velocity into meters per second (m/s):
Velocity of train (vs) = 36 km/h = 36 × (1000 m / 3600 s) = 10 m/s
The formula for the frequency of the echo heard by the train driver is given by:
fecho = f0 × [(v + v0) / (v - vs)]
where:
f0 = original frequency = 320 Hz,
v = speed of sound = 330 m/s,
v0 = observer's velocity, since the train and observer are the same, v0 = vs = 10 m/s,
Substitute the values into the formula:
fecho = 320 × [(330 + 10) / (330 - 10)]
fecho = 320 × [(340) / (320)]
Calculate the value:
fecho = 320 × 1.0625 = 340 Hz
Thus, the frequency of the echo heard by the train driver is 340 Hz, which falls within the expected range of 340 to 340 Hz. The calculation confirms that the computed frequency matches the expected value in the given range.
Approach Solution -2
The frequency that reaches the hill will reflect, and this will act as a source to the driver of the train.
The apparent frequency that reaches the hill =\(\frac{330}{330-10}\)(320)=330Hz, this will act as a source for the driver.
Apparent frequency heard by the driver in train =\(\frac{330+10}{330}\)(330)=340 Hz
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Concepts Used:
Waves
Waves are a disturbance through which the energy travels from one point to another. Most acquainted are surface waves that tour on the water, but sound, mild, and the movement of subatomic particles all exhibit wavelike properties. inside the most effective waves, the disturbance oscillates periodically (see periodic movement) with a set frequency and wavelength.
Types of Waves:
Transverse Waves -
Waves in which the medium moves at right angles to the direction of the wave.
Examples of transverse waves:
- Water waves (ripples of gravity waves, not sound through water)
- Light waves
- S-wave earthquake waves
- Stringed instruments
- Torsion wave
The high point of a transverse wave is a crest. The low part is a trough.
Longitudinal Wave -
A longitudinal wave has the movement of the particles in the medium in the same dimension as the direction of movement of the wave.
Examples of longitudinal waves:
- Sound waves
- P-type earthquake waves
- Compression wave