Ch09 Wave

PHYSICS 1ST PAPER CHAPTER 9 Wave Question 1 Rafique and Shafique are two friends. One afternoon they were gossiping, sitting by the side of a lake. Cold breeze was blowing. Beautiful waves were playing in the water of the lake. Sound is a kind of wave which has wavelength, frequency, velocity and intensity. (a) What is a wave? (b) Establish the relation among wave velocity, frequency and wavelength. (c) The difference of wavelengths of two waves of frequencies 480 Hz and 320 Hz in a certain medium is 2 m. Find the velocity of sound in the medium. (d) On what factors does the intensity of sound depend? What will happen to the intensity of sound if the density of the medium decreases during the propagation of sound? Explain with reasons. Solution (a) A periodic disturbance that carries energy through a medium is called a wave. (b) Let a wave have the frequency 𝑓, the wavelength 𝜆and the velocity 𝑣. 𝑥 𝜆 𝑣 A source completes one vibration in the time period 𝑇. In this time the wave moves forward by one wavelength. 𝑣= distance time = 𝜆 𝑇 The frequency is the number of vibrations in one second, so 𝑓= 1 𝑇. 𝑣= 𝑓𝜆 (c) Here, Frequency of the first wave 𝑓1 = 480 Hz Frequency of the second wav

longer wavelength. 𝜆2 −𝜆1 = 𝑣 𝑓2 −𝑣 𝑓1 2 = 𝑣  1 320 − 1 480  2 = 𝑣× 1 960 𝑣= 1920 m s−1 𝑣= 1920 m s−1 (d) The intensity of a sound wave is 𝐼= 2𝜋2𝜌𝑣𝑓2𝑎2 Here 𝜌is the density of the medium and 𝑣is the velocity of sound. The frequency is 𝑓and the amplitude is 𝑎. Thus the intensity depends on four factors. Factor Relation Amplitude of vibration 𝐼∝𝑎2 Frequency of the wave 𝐼∝𝑓2 Density of the medium 𝐼∝𝜌 Velocity of sound in the medium 𝐼∝𝑣 For the same source, 𝑓and 𝑎stay fixed. The intensity is then proportional to the density. 𝐼∝𝜌 A medium of lower density has less mass in each unit volume. Less energy then passes through unit area in each second. Hence the intensity of sound decreases when the density decreases. ahbab.dev 2

Question 2 The waves spread out in the calm water of a lake when Pretha throws a stone. The wave started to go 5 cm up and down from the stationary position. (a) What is resonance? (b) What do you mean by intensity level? (c) Express the wave produced in the lake as 𝑦= 𝑎sin 2𝜋 𝜆(𝑣𝑡−𝑥). The time period and wavelength of the wave were 0.04 s and 20 cm. (d) Compare the wave velocity with the instantaneous velocity of a vibrating particle after 10 s at a distance of 5 m from the place where the stone fell into the water. Solution (a) Resonance is a forced vibration in which the applied frequency equals the natural frequency. (b) The intensity of a sound is compared with a standard intensity 𝐼0. The logarithm of this ratio is called the intensity level. 𝛽= 10 log10 𝐼 𝐼0 dB Here 𝐼0 = 1 × 10−12 W m−2 is the faintest intensity that the ear can hear. The unit of intensity level is the decibel. A sound of intensity 𝐼0 has a level of 0 dB. (c) Here, Amplitude 𝑎= 5 cm = 0.05 m Time period 𝑇= 0.04 s Wavelength 𝜆= 20 cm = 0.20 m The velocity of the wave is 𝑣= 𝜆 𝑇= 0.20 0.04 m s−1 = 5 m s−1 Putting the values of 𝑎, 𝜆and 𝑣in the given equation, 𝑦= 𝑎sin 2𝜋 𝜆(𝑣𝑡−𝑥) = 0.05 sin 2𝜋 0.20 (5𝑡−𝑥) = 0.05 s