## Pages

### Conceptual Questions of waves

1. Transverse wave velocity in a stretched string depends on
a. frequency of wave
b. tension
c. length of string
d. linear mass density string

2. A transverse wave travels along the x axis.The particles of the medium must move
a. Along the z-axis
b Along the x-axis
c. In the Y-Z plane
d. Along the y axis

3.What is true for a standing wave on the string
a.All the particles are never at rest simultaneously
b. In one complete cycle,all the particles cross their mean position simultaneously twice
c. In one complete cycle,all the particles cross their mean position simultaneously once
d. All the particles acquire their positive extreme positions simultaneously once in a cycle

4.Choose the incorrect one
a. When a ultrasonic wave travels from air into water.It bends towards the normal to the air-water interface
b.Any function of the form y(x,t)=f(vt+x) represents a travelling wave
c.the velocity ,wavelenght and frequency of wave undergo change when it is reflected from a surface
d. None of the above

5.Match the following with the types of the wave

B)Sound waves produced by the vibrating string of guitar
D)X Rays
E) Waves produced in the air by the vibrating tuning fork

P) longitudinal
Q) Transverse

6. Which of the following functions represent a travelling wave
a. y=pcos(qx)sin(rt)
b. y=psin(qx+rt)
c. y=psin(qx-rt)
d. none of the above

7. Which of the following is not a standing wave
a. y=pcos(qx)sin(rt)
b. y=psin(qx+rt)+psin(qx-rt)
c. y=psin(qx+rt)
d Non of the above

8. When a wave is refracted into another medium which of the following will change
a. Velocity
b. Frequency
c. Phase
d. Amplitude

9.A pipe closed at one end and open at other will give
a. All even harmonics
b, All odd harmonics
c. All the harmonics
d. None of the harmonics

10. To raise the pitch of a stringed musical instrument ,the player can
a. Lossen the string
b. Tighten the string
c. Shorten the string
d. Lengthen the string

Solutions

### Waves Concept

PART 3

Beats:-
-Interference of two harmonic waves of different frequencies and wavelength produces beats.
-In beats phenomenon interfering harmonic waves have slightely differing frequencies ν1 and ν2 such that
12|<<(ν12)/2
-Thus beats arises when two waves having slightly differing frequencies ν1 and ν2 and comparable amplitude are superposed. The beat frequency is
νbeat= ν1 ∼ ν2
-Musicians use beat phenomenon for tuning their instruments.
-For tuning an instrument for certain standard frequency it is sounded against a standard frequency and it is tuned untill the beats get disappeared.

Doppler effect:-
-Doppler effect is a change in the observed frequency of the wave when the source s and the observer o moves relative to the medium.
-There are three different ways where we can analyse this change in frequency.
(1) When observer is stationary and source is moving then change in frequency for source aproaching observer is
ν=ν0(1+vs/v)
where, vs=velocity of source relative to the medium
v=velocity of wave relative to the medium
ν=observed frequency of sound waves in term of source frequency
ν0=source frequency
-Change in frequencywhen source receeds from stationary observer is
ν=ν0(1-vs/v)
-Observer at rest measures higher frequency when source aproaches it and it measures lower frequency when source receeds from the observer.
(2)Doppler effect in frequency when observer is moving with a velocity vo towards source and the source is at rest is
ν=ν0(1+vo/v)
(3) If both source and observer are moving then frequency observed by observer is
ν=ν0(v+vo)/(v+vs)
and all the symbols have respective meanings as told earlier.