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:<br />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.<br />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.<br />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.<br /><br />Broad/Descriptive Questions:<br />1. The equation of a progressive wave can be derived as $y(x,t)=Acos(kx-\omega t)$, where $A$ is the amplitude, $k$ is the wave number, and $\omega$ is the angular frequency.<br />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).<br />3. The fundamental frequency of a standing wave is given by $f_{n}=\frac {n}{2L}\sqrt {\frac {r}{\mu }}$, where $n$ is the mode number, $L$ is the length of the medium, $r$ is the linear mass density, and $\mu$ is the tension per unit length.<br />1. i. The frequency is 10.5 Hz, the angular frequency is 3.14/s, and the propagation constant is 0.031/cm.<br />ii. The equation of the wave is $y=10sin(\frac {\pi x}{100}-\pi t)$.<br />iii. The equation of the motion of the left end of the string is $y=-10sin(\pi t)$.<br />iv. The equation of a particle 150 cm to the right of the string is $y=10sin(\frac {3\pi }{2}-\pi t)$.<br />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.<br />ii. The wave function describing the wave is $y=0.01sin(31.4t-3.14x)$.<br />iii. The position of the point at $x=0.25m$ at time $t=0.1$ second is 0.00707 m.<br />iv. The transverse velocity of the point at $x=0.25m$ at time $t=0.1$ second is -0.22 m/s.<br />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.<br />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.<br />5. (a) The fundamental frequency of the steel piano wire is 200 Hz.<br />(b) The highest overtone that could be heard by a person capable of hearing frequencies up to 10000 Hz is 50.