Subject: Science
When the displacement of a particle is maximum above from its mean position, the particle is said to be at the crest of the wave and when the displacement of a particle is maximum below the mean position, the particle is said to be at the trough. The transverse wave travels in the form of trough and crest.
TheLongitudinal wave travels in the form of compression and rarefaction. In compression, particles of medium get compressed and in rarefaction density is less than normal density. In another way, the region where the medium is compressed is known as a compression and the region where the medium is spread out is known as a rarefaction.
One crest and one trough constitute one complete wave in a transverse wave. One compression and one rarefaction constitute one complete wave in a longitudinal wave.
The maximum displacement of a particle from its mean position in a wave is called amplitude of that wave. Its SI unit is ‘m’.
The number of complete waves, set up in a medium in one second is called frequency of the wave. Its SI unit is hertz (Hz).
The time taken by wave to complete one cycle or a complete wave is called time period. Its unit is second.
The distance between two consecutive troughs or crests in a transverse wave or the distance between two consecutive compressions or rarefactions in a longitudinal wave is called wavelength. Its SI unit is meter (m).
The velocity with which wave propagates in a medium is called wave velocity. Its SI unit is m/s.
The formula showing the relation between v, f and λ is called wave equation. The product of frequency and wavelength is equal to wave velocity.
Wave velocity (v) = frequency (f) × wavelength (λ)
The number of complete waves, set up in a medium in one second is called frequency of the wave. Its SI unit is hertz (Hz). According to the definition of frequency,
f vibrations are completed in one second.
Or, 1 vibrations is completed in \(\frac{1}{f}\) second.
But, time to complete one vibrationis its time period (T)
\(\therefore\) T = \(\frac{1}{f}\)
time period = \(\frac{1}{frequency}\) |
One crest and one trough in transverse wave and one compression and one rarefaction in longitudinal wave is called a complete wave.
Solution:
Here,
Speed of sound (v) = 340m/s
Wavelength (λ) = 2.4cm = 0.024m
Frequency of sound (f) = ?
We know,
v = λ x f
or, f =
or, f =
Solution:
Here,
Speed of sound (v) = 332m/s
Wavelength (λ) = ?
Frequency of sound (f) = 20Hz
We know,
v = λ x f
or, λ =
or, λ =
Solution:
Here,
Speed of sound (v) = 340m/s
Shortest Wavelength (λ) = ?
Highest Frequency of sound (f) = 20KHz = 20 x 1000 = 20000Hz
We know,
v = λ x f
or, λ =
or, λ =
∴ λ = 0.017m
Hence, the shortest wavelength is 0.017m
Again similarly,
We have,
Speed of sound (v) = 340m/s
Longest Wavelength (λ) = ?
lowest Frequency of sound (f) = 20Hz
We know,
v = λ x f
or, λ =
or, λ =
∴ λ = 17m
Hence, the longest wavelength is 17m
Solution:
Here,
Total number of complete wave (n) = 20
Time (t) = 4s
Frequency (f) = ?
We have,
f = = 20/4 = 5 Hz
Also, the distance between two crests is 3 cm
So, wavelength (λ) = 3/100 = 0.03m
Again,
Wave speed (v) = wavelength (λ) x frequency (f)
= 0.03 x 5
= 0.15m/s
Medium | Velocity |
A | 400m/s |
B | 900m/s |
C | 700m/s |
Person | Frequency |
A | 900Hz |
B | 550Hz |
C | 400Hz |
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