## F.Sc ICS Notes: Physics XI: Chapter 8 Waves Numerical Problems

__The wavelength of the signals from a radio transmitter is 1500m and the frequency is 200Khz. What is the wavelength for a transmitter operating at 1000Khz and with what speed the radio waves travel.__

**Numerical Problem 8.1:**__Two speakers are arranged as shown in figure. The distance between them is 3m and they emit a constant tome of 344Hz. A microphone P is moved along a line parallel to and 4m from the line connecting the two speakers. It is found that tone of maximum loudness is heard and displayed on the CRO when microphone is on the center of the line and directly opposite each speakers. Calculate the speed of sound.__

**Numerical Problem 8.2:**__A stationary wave is established in a string, which is 120cm long and fixed at both ends. The string vibrates in four segments, at a frequency of 120Hz. Determine its wavelength and the fundamental frequency.__

**Numerical Problem 8.3:**__The frequency of the note emitted by a stretched string is 300Hz. What is the frequency of this note when: (a) Length of the wave is reduced by one third without changing tension, (b) The tension is increased by one-third without changing the length of the wire.__

**Numerical Problem 8.4:**__An organ pipe has a length of 50cm. Find the frequency of its fundamental note and the next harmonic when it is: (a) Open at both ends. (b) Closed at one end (speed of sound = 350m/s).__

**Numerical Problem 8.5:**__A church organ consists of pipes, each open at one end, of different lengths. The minimum length is 30mm and the longest is 4m. Calculate the frequency range of fundamental notes. (speed of sound = 340m/s).__

**Numerical Problem 8.6:**__Two tuning forks exhibit beats at a beat frequency of 3Hz. The frequency of one fork is 256Hz. Its frequency is then lowered slightly by adding a bit of wax to one of its prong. The two forks then exhibit a beat frequency of 1Hz. Determine the frequency of second tuning fork.__

**Numerical Problem 8.7:**__Two cars P and Q are traveling along a motorway in the same direction. The leading car P travels at a steady speed of 12m/s, the other car Q, traveling at a steady speed of 20m/s, sound its horn to emit a steady note which P's driver estimates has a frequency of 830 Hz. What frequency does Q's own driver hear? (Speed of sound = 340 m/s)__

**Numerical Problem 8.8:**__A train sounds its horn before it sets off from the station and an observer waiting on the platform estimates its frequency at 1200 Hz. The trains then moves off and accelerates steadily. Fifty seconds after departure, the driver sounds the horn again and the platform observer estimates the frequency of 1140 Hz. Calculate the train speed 50 s after departure. How far from the station is the train after 50 s? (Speed of sound = 340 m/s).__

**Numerical Problem 8.9:**__The absorption spectrum of light galaxy is measured and the wavelength of one of the lines identified as the calcium line is found to be 478 nm. The same line has a wavelength of 397 nm when measured in a laboratory. (a) Is the galaxy moving towards or away from the earth? (b) Calculate the speed of the galaxy relative to Earth (Speed of light 3 x 10(8)m/s).__

**Numerical Problem 8.10****:**
nice numerical

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