What are the intensity and wave properties of two simple wave problems?

[saksham]

**** Intensity and spherical waves*****
Sound waves are spreading out equally in all directions from a points source. You measure an intensity of 0.026 W/m2 at a distance of 4.3 m from the source.
a) What is the intensity in a distance of 3.1 m from the source?

b) How much sound energy does the source emit in one hour assuming that the power output stays constant?

******Mathematical description of a wave:******

A transverse wave on a string can be described by:
Y(x,t)= A cos [k(x-vt)]

a) Find the maximum transverse speed vy of a particle of the string. Under that circumstances is it equal to the propagation speed of the wave?

b) The wave has an amplitude of 0.300 cm, wavelength 12.0 cm, and speed 6.00 cm/s. What is its frequency? What is the deflection of a particle of the string at time t = 5 s and position x = 10 cm?

Please help me out!

 

[Nylex]

**** Intensity and spherical waves*****
Sound waves are spreading out equally in all directions from a points source. You measure an intensity of 0.026 W/m2 at a distance of 4.3 m from the source.
a) What is the intensity in a distance of 3.1 m from the source?

b) How much sound energy does the source emit in one hour assuming that the power output stays constant?

For a., can you not use the fact that intensity is inversely proportional to area? I = P/A^2=> IA^2 = P. Seeing as it is the same point source, the power will be the same. You can then write I1(A1)^2 = I2(A2)^2 and use this to find I2 (I1, A1 being the intensity and area at 4.3 m, I2 and A2 being the intensity and area at 3.1 m). The waves will spread out over a sphere, so use the distances you're given as the radii of the spheres and you can calculate the area. At least, I think that's how you would do it.

b. Use P = E/t and get the power from the information you're given above.

Not sure about the wave equations, so sorry about that.

 

[saksham]

Thanks Nylex!

Could anyone solve the other one for me, please! I need it desperately.

 

[saksham]

Help me people! I have to meet the deadline tomorrow.