Question

(a) A woman is standing in the ocean, and she notices that after a wave crest passes by, six more crests pass in a time of 47.2 s. Calculate the period of the wave.

(b) If two whistles are blown simultaneously, with respective frequencies of 505 Hz and 501 Hz, evaluate the beat frequency that is heard.

(c) The speed of a transverse wave on a string is 110 m s−1 . The tension in the string is 340 N. Calculate the mass per unit length of the string.

(d) As you stand on the pavement, a vehicle approaches you at a speed of 45 m s−1 , sounding its horn at a frequency of 8000 Hz. Calculate the frequency of sound that you hear.

(e) A laser emits a narrow beam of light. The radius of the beam is 7.5 mm, and the power is 3.7 mW. Calculate the intensity of the laser beam.

(f) An object of height 3.0 cm is placed 26 cm in front of a convex mirror with a radius of curvature of 16 cm. Find the location and height of the image.

Answer 1

a) six wave crests travel in 47.2 seconds

hence period T = 47.2/6 = 7.86 s

b) given n₁ = 505 Hz and n₂ = 501 Hz

beat frequency = n₁ - n₂  

= 505 - 501

= 4 Hz

c) given v = 110 m/s and T =340N

v² = T/m

hence mass per unit length m = T/v²

= 340 / ( 110 x 110 )

= 0.028 kg/m

d) velocity v = 45m/s

velocity of sound in air c = 340m/s

sound frequency n = 8000Hz

required frequency f = (c/c-v).n

= (340/340-45) x 8000

= 9220.3 Hz

e) r= 7.5mm = 7.5 x 10^-3 m P = 3.7 mW = 3.7 x 10^-3 W

intensity I = P/Area

= P / pi.r²

= 3.7 x 10^-3 / (3.14 x 7.5 x 10^-3 x 7.5 x 10^-3)

= 20.95 W/m²