Short Questions: 1. Differentiate between mechanica I and electromagnetic wave 2. Differentiate between longitudinal and transverse wave. 3. State the principle of superposition of waves. Broad/Descriptive Questions: 1. Derive the equation of a progressive wave or prove that y(x,t)=Acos(kx-omega t) 2. Explain Standing wave Find the position of Node and antinode in a standing eave 3. Find the fundamental frequency of a standing wave or prove that f_(n)=(n)/(2L)sqrt ((r)/(mu )) 1. A transverse sine wave of amplitude 10 cm and wavelength 200 cm travels from left to right along a long horizontal string with a speed 100cm/s Take the origin at the left end. At time t=0. the left end of the string is at the origin and is moving downward i. Find the frequency, angular frequency, and propagation constant.10.5 Hz, 3.14/s 0.031/cm] ii. What is the equation of the wave? y=10sin((pi x)/(100)-pi t)1 iii. What is the equation of motion of the left end of the string? [y=-10sin(pi t)] Page 6 of 14 PHY 101: Chapter 8 iv. What is the equation of a particle 150 cm to the right of the string? y=10sin((3pi )/(2)- pi t) 2. A certain string has a linear mass density of 0.25kg/m and is stretched with a tension of 25 N. One end is given a sinusoidal motion with frequency 5 Hz and amplitude 0.01 m. Att=0 the end has zero displacement and is moving in the +y direction. i. Find the wave speed.amplitude, angular frequency, period wavelength and wave number [10m/s,0.01m,31.4/s,0.2s,2m,3.14/m] ii. Write a wave function describing the wave. [y=0.01sin(31.4t-3.14x)] iii. Find the position of the point at x=0.25m at time t=0.1 second. [0.00707m] iv. Find the transverse velocity of the point at x=0.25m at time. t=0.1 second. [-0.22 m/s] 3. The equation of a transverse traveling wave on a string is y=2cos[pi (0.5x-200t)] where x and y are in centimeters and t is in seconds.Find the wavelength, frequency.time period and velocity of propagation. 2cm,100Hz,0.01s,400cm/s 4. The equation of a transverse traveling wave on a string is, y=2sin2pi ((t)/(0.01)-(x)/(30)) where x and y are expressed are in cm and t is in seconds. Find the amplitude, wavelength, frequency, period and velocity of the propagation. [2 cm.30 cm, 100 Hz,3000cm/s] 5. A steel piano wire 50 cm long of mass 5 g is stretched with a tension of 400 N (a) What is its fundamental frequency? [200 H2] (b) What is the number of the highest overtone that could be heard by a person who is capable of hearing frequencies up to 10000 Hz? [50]

Short Questions:1. Mechanical waves require a medium for propagation and involve the vibration of particles in the medium, while electromagnetic waves can propagate in a vacuum and involve oscillating electric and magnetic fields.2. In a longitudinal wave, particles of the medium move parallel to the direction of wave propagation, while in a transverse wave, particles move perpendicular to the direction of wave propagation.3. The principle of superposition of waves states that when two or more waves meet, the resulting wave is the algebraic sum of the individual waves.Broad/Descriptive Questions:1. The equation of a progressive wave can be derived as , where is the amplitude, is the wave number, and is the angular frequency.2. A standing wave is formed when two waves of the same frequency and amplitude travel in opposite directions, resulting in nodes (points of minimum amplitude) and antinodes (points of maximum amplitude).3. The fundamental frequency of a standing wave is given by , where is the mode number, is the length of the medium, is the linear mass density, and is the tension per unit length.1. i. The frequency is 10.5 Hz, the angular frequency is 3.14/s, and the propagation constant is 0.031/cm.ii. The equation of the wave is .iii. The equation of the motion of the left end of the string is .iv. The equation of a particle 150 cm to the right of the string is .2. i. The wave speed is 10 m/s, the amplitude is 0.01 m, the angular frequency is 31.4/s, the period is 0.2 s, the wavelength is 2 m, and the wave number is 3.14/m.ii. The wave function describing the wave is .iii. The position of the point at at time second is 0.00707 m.iv. The transverse velocity of the point at at time second is -0.22 m/s.3. The wavelength is 2 cm, the frequency is 100 Hz, the time period is 0.01 s, and the velocity of propagation is 400 cm/s.4. The amplitude is 2 cm, the wavelength is 30 cm, the frequency is 100 Hz, the period is 0.01 s, and the velocity of propagation is 3000 cm/s.5. (a) The fundamental frequency of the steel piano wire is 200 Hz.(b) The highest overtone that could be heard by a person capable of hearing frequencies up to 10000 Hz is 50.