A small sphere of radius R is arranged to pulsate so that its radius varies in simple harmonic motion between a minimum of R−x and a maximum of R+x with frequency f. This produces sound waves in the surrounding air of density rho and bulk modulus B.

a- Find the intensity of sound waves at the surface of the sphere. (The amplitude of oscillation of the sphere is the same as that of the air at the surface of the sphere.)

b-Find the total acoustic power radiated by the sphere

c-At a distance d≫R from the center of the sphere, find the amplitude of the sound wave.

d-At a distance d≫R from the center of the sphere, find the pressure amplitude of the sound wave.

e-At a distance d≫R from the center of the sphere, find the intensity of the sound wave.

Express your answer in terms of the variables R, x, f, and appropriate constants.

Aheat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. the same engine running backward is called a heat pump if its purpose is to exhaust warm air into the hot reservoir. heat pumps are widely used for home heating. you can think of a heat pump as a refrigerator that is cooling the already cold outdoors and, with its exhaust heat qh, warming the indoors. perhaps this seems a little silly, but consider the following. electricity can be directly used to heat a home by passing an electric current through a heating coil. this is a direct, 100% conversion of work to heat. that is, 19.0 \rm kw of electric power (generated by doing work at the rate 19.0 kj/s at the power plant) produces heat energy inside the home at a rate of 19.0 kj/s. suppose that the neighbor's home has a heat pump with a coefficient of performance of 4.00, a realistic value. note: with a refrigerator, "what you get" is heat removed. but with a heat pump, "what you get" is heat delivered. so the coefficient of performance of a heat pump is k=qh/win. an average price for electricity is about 40 mj per dollar. a furnace or heat pump will run typically 200 hours per month during the winter. what does one month's heating cost in the home with a 16.0 kw electric heater? what does one month's heating cost in the home of a neighbor who uses a heat pump to provide the same amount of heating?

The speed of light can be used to measure the

A0.580-kg rock is tied to the end of a string and is swung in a circle with a radius of 0.500 meters. the velocity of the rock is 4.50 m/s. what is the centripetal force acting on the rock? 15.5 n 5.22 n 69.8 n 23.5 n