Wave motion

Question 1

What is the formulaic representation of velocity of wave in stretched string?

Answer 1

Velocity of wave in stretched string is given by:

v=√T/m

Question 2

What is the formulaic representation of Speed of sound wave in solid rod?

Answer 2

The Speed of sound wave in solid rod is given by:
v=√Y/d
; Y= Young Modulus

Question 3

What is the formulaic representation of Speed of sound wave in liquid?

Answer 3

The Speed of sound wave in liquid is given by:
v=√B/d
; B= Bulk Modulus

Question 4

What is the formulaic representation of Speed of sound wave in gas according to Newton’s Formula?

Answer 4

The Speed of sound wave in gas is given by:

v= √P/d (Laplace’s Correction)

Question 5

What is the effect of density in Speed of sound wave?

Answer 5

Speed of Sound Wave v ~ (1/√d)

v1/v2 = √d2/d1

Question 6

What is the effect of molecular weight in Speed of sound wave?

Answer 6

Speed of Sound Wave v ~ (1/√M)

v1/v2 = √M2/M1

Question 7

What is the equation of traveling wave?

Answer 7

Equation of travelling wave is given by:
y = a sin ωt
; a = Amplitude
ω(=2πn) is angular velocity

Question 8

What is the relation between Path difference and Phase difference?

Answer 8

phase difference = 2π/ λ x path difference
or
Δ∅ = 2π/λ x Δx
where Δ∅=(∅1-∅2) is the phase difference between those two particle is separated by a distance Δx = (x2-x1)

Question 9

What is the relation between Intensity of Wave to amplitude or vibration and frequency of vibration?

Answer 9

Intensity of Wave(I) is proportional to the square of amplitude (a²) of vibration and square of frequency (n²) of vibration

Question 10

In case of vibration of stretched string with both ends fixed, what is the relation of frequency ?

Answer 10

In case of vibration of stretched string with both ends fixed v=nb/2l
n1=v/λ1= 1/2l √T/m( First Harmonic )

Question 11

In case of vibration of stretched string with one end fixed, what is the relation of frequency ?

Answer 11

In case of vibration of stretched string with one end fixed:
v= (n+1/2) v/2L
v°= v/4L( First Harmonic )

Question 12

According to laws of transverse vibrations of a string, what is the relation of frequency with length, tention and mass?

Answer 12

v~1/L if F and μ are constants
v~√F if L and μ are constants
v~1/√μ if F and L are constants