| Numerical Problems |
Q.10.3 Find the time periods of a simple pendulum of 1 metre length, placed on Earth and on Moon. The value of g on the surface of Moon is 1/6 of its value on Earth,
where g is 10 m s-2 .
Q. 10.7 A transverse wave produced on a spring has a frequency of 190 Hz and travels along the length of the spring of 90 m, in 0.5 s.
(a) What is the period of the wave?
(b) What is the speed of the wave?
(c) What is the wavelength of the wave?
Q.10.8 Water waves in a shallow dish are 6.0 cm long. At one point, the water moves up and down at a rate of 4.8 oscillations per second.
(a) What is the speed of the water waves?
(b) What is the period of the water waves?
Q.10.10 What is the wavelength of the radio waves transmitted by an FM station at 90 MHz? where 1M = 106 , and speed of radio wave is 3 x 108 m s-1 .
Q.10.1 The time period of a simple pendulum is 2 s. What will be its length on the Earth? What will be its length on the Moon if gm = ge /6? where ge = 10 m s-2
Q.10.2 A pendulum of length 0.99 m is taken to the Moon by an astronaut. The period of the pendulum is 4.9 s. What is the value of g on the surface of the Moon?
Q.10.3 Find the time periods of a simple pendulum of 1 metre length, placed on Earth and on Moon. The value of g on the surface of Moon is 1/6 of its value on Earth, where g is 10 m s-2 .
Tm = 2 x ( 3.14 ) x ( 0.774 )
Tm = 4.9 sec. Time period on Moon.
Q.10.4 A simple pendulum completes one vibration in two seconds. Calculate its length, when g = 10.0 m s-2 .
Solution: Given Data:
Q.10.5 If 100 waves pass through a point of a medium in 20 seconds, what is the frequency and the time period of the wave? If its wavelength is 6 cm, calculate the wave speed.
Q. 10.6 A wooden bar vibrating into the water surface in a ripple tank has a frequency of 12 Hz. The resulting wave has a wavelength of 3 cm. What is the speed of the wave?
Solution: Given Data:
Frequency f = 12 Hz
Wavelength λ = 3cm = 0.03m we know 1 m = 100 cm
Speed v = ?
Formula: v = f λ
v = (12) x (0.03)
Q. 10.7 A transverse wave produced on a spring has a frequency of 190 Hz and travels along the length of the spring of 90 m, in 0.5 s.
(a) What is the period of the wave?
(b) What is the speed of the wave?
(c) What is the wavelength of the wave?
Solution: Given Data:
Frequency f = 190 Hz
Wavelength λ = 3cm = 0.03m we know 1m = 100 cm
Length of the spring d = 90m
(a) T = ? (b) Speed v = ? (c) Wavelength λ = ?
(a)
Formula: f = 1/T
T = 1/f = 1/190
T = 0.01 second
(b)
Formula: d = vt
v = d/t
v = 90/0.5
v = 180 ms-1
(c)
Formula: v = f λ
λ = v/f
λ = 180/190
Q.10.8 Water waves in a shallow dish are 6.0 cm long. At one point, the water moves up and down at a rate of 4.8 oscillations per second.
(a) What is the speed of the water waves?
(b) What is the period of the water waves?
Solution: Given Data:
Length of waves (wavelength) λ = 6.0cm = 0.06m we know that 1m = 100cm
No. of oscillation frequency f = 4.8Hz
(a) Speed v = ? (b) Period T = ?
(a)
Formula: f = 1/T
T = 1/f
T = 1/4.8 = 0.21 second
(b)
Formula: v = f λ
v = (4.8) x (0.06)
Q.10.9 At one end of a ripple tank 80 cm across, a 5 Hz vibrator produces waves whose wavelength is 40 mm. Find the time the waves need to cross the tank.
Solution: given Data:
Length of ripple tank d = 80cm = 0.8 m we know that 1m = 100cm
Frequency f = 5 Hz
Wavelength λ = 40mm = 0.04m we know that 1m = 1000mm
Time to cross the wave t = ?
First we find the speed of wave v = ?
Formula v = f λ
Putting the values we get v = (5) x (0.04)
v = 0.2 ms-1
Formula d = vt
t = d/v
t = 0.8/0.2
Q.10.10 What is the wavelength of the radio waves transmitted by an FM station at 90 MHz? where 1M = 106 , and speed of radio wave is 3 x 108 m s-1 .
Solution: Given data:
Frequency f = 90MHz (Given 1M = 106 )
Speed of radio waves is v= c = 3 x 108 ms-1
Formula v = c = f λ
λ = c/f
λ = 3 x 108/90 x 106
λ = 3 x 108 / 90 x 106
λ = 3.33m