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A vibrating tuning fork generates a wave given by y = 0.1 sinπ (0.1x - 2t), where x and y are in metre and t is in seconds. The distance travelled by the wave while the fork completes 30 vibrations is
- a)600 m
- b)20 m
- c)36 m
- d)200 m
Correct answer is option 'A'. Can you explain this answer?
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A vibrating tuning fork generates a wave given by y = 0.1 sinπ (0.1...
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A vibrating tuning fork generates a wave given by y = 0.1 sinπ (0.1...
(200πt), where y is the displacement of the wave from its equilibrium position in meters and t is the time in seconds.
The amplitude of the wave is 0.1 meters, which is the maximum displacement from the equilibrium position. The frequency of the wave is 200 cycles per second, or 200 Hz, which is the number of complete oscillations the wave makes in one second.
The wavelength of the wave can be calculated using the formula:
λ = v/f
where λ is the wavelength in meters, v is the speed of the wave in meters per second, and f is the frequency in Hz. The speed of the wave in a medium depends on the properties of the medium, such as its density and elasticity. For simplicity, let's assume that the wave is traveling in air at room temperature and pressure, where the speed of sound is approximately 343 meters per second.
λ = 343/200 = 1.715 meters
This means that the distance between two consecutive points on the wave that are in phase (such as two peaks or two troughs) is 1.715 meters.
The period of the wave can be calculated using the formula:
T = 1/f
where T is the period in seconds. In this case, the period is:
T = 1/200 = 0.005 seconds
This means that the wave completes one full cycle (i.e. goes from its maximum displacement to its minimum displacement and back to its maximum displacement again) in 0.005 seconds.
The speed of the wave can also be calculated using the formula:
v = λ/T
v = 1.715/0.005 = 343 meters per second
This confirms that the speed of the wave in air at room temperature and pressure is approximately 343 meters per second, which is the same as the speed of sound in air at those conditions.
The amplitude of the wave is 0.1 meters, which is the maximum displacement from the equilibrium position. The frequency of the wave is 200 cycles per second, or 200 Hz, which is the number of complete oscillations the wave makes in one second.
The wavelength of the wave can be calculated using the formula:
λ = v/f
where λ is the wavelength in meters, v is the speed of the wave in meters per second, and f is the frequency in Hz. The speed of the wave in a medium depends on the properties of the medium, such as its density and elasticity. For simplicity, let's assume that the wave is traveling in air at room temperature and pressure, where the speed of sound is approximately 343 meters per second.
λ = 343/200 = 1.715 meters
This means that the distance between two consecutive points on the wave that are in phase (such as two peaks or two troughs) is 1.715 meters.
The period of the wave can be calculated using the formula:
T = 1/f
where T is the period in seconds. In this case, the period is:
T = 1/200 = 0.005 seconds
This means that the wave completes one full cycle (i.e. goes from its maximum displacement to its minimum displacement and back to its maximum displacement again) in 0.005 seconds.
The speed of the wave can also be calculated using the formula:
v = λ/T
v = 1.715/0.005 = 343 meters per second
This confirms that the speed of the wave in air at room temperature and pressure is approximately 343 meters per second, which is the same as the speed of sound in air at those conditions.
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A vibrating tuning fork generates a wave given by y = 0.1 sinπ (0.1x - 2t), where x and y are in metre and t is in seconds. The distance travelled by the wave while the fork completes 30 vibrations isa)600 mb)20 mc)36 md)200 mCorrect answer is option 'A'. Can you explain this answer?
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