A periodic longitudinal wave is sent
on a slinky. The wave proceeds at a
speed of 48 cm/s and each particle
oscillates at a frequency of 12 Hz.
Calculate the minimum separation
between the positions where the
slinky is most compressed.
please answer it fast
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Physics
A longitudinal wave is produced on a toy slinky. The wave travels at a speed of 30 cm/s and the frequency of the wave is 20 Hz. What is the minimum separation between the consecutive compressions of the slinky?
A .
0.015m0.015m
B .
0.03m0.03m
C .
0.045m0.045m
D .
0.06m0.06m
December 20, 2019avatar
Mounika Waswani
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ANSWER
The relationship between the frequency, wavelength and speed of sound or velocity is given as follows.
Frequency\quad \nu =\dfrac { wave\quad velocity\quad v }{ wavelength\quad \lambda } Frequencyν=
wavelengthλ
wavevelocityv
From the above equation, wavelength is derived as, Wavelength\quad \lambda =\dfrac { wave\quad velocity\quad v }{ Frequency\quad \nu } Wavelengthλ=
Frequencyν
wavevelocityv
In the question, the velocity of sound is 30 cm/s, that is 0.3 m/s and frequency=20 Hz is given.
The distance between two consecutive compression is equal to the wavelength of the wave, therefore,
Wavelength\quad \lambda =\dfrac { v }{ \nu } =\dfrac { 0.3\quad m/s }{ 20\quad Hz } =0.015\quad mWavelengthλ=
ν
v
=
20Hz
0.3m/s
=0.015m.
Hence, the wavelength of the sound wave is given as 0.015 m.
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