ive been trying these problems from some time now and i still am unable to get s

Question

ive been trying these problems from some time now and i still am unable to get some. others i have the answer but i do not know the process so please explain :) even answering one will be a great help! thank you!

1.) A transverse wave on a string has an amplitude of 0.23 m and a frequency of 165 Hz. Consider the particle of the string at x = 0 m. It begins with a displacement of y = 0 m when t = 0 s, according to the following. y = A sin 2ft 2x y = A sin 2ft + 2x How much time passes between the first two instants when this particle has a displacement of y = 0.2 m?

2.) A sound wave is incident on a pool of fresh water (20° C). The sound enters the water perpendicularly and travels a distance of 0.52 m before striking a 0.17-m-thick copper block lying on the bottom. The sound passes through the block, reflects from the bottom surface of the block, and returns to the top of the water along the same path. How much time elapses between when the sound enters and when it leaves the water?

3.) A monatomic ideal gas ( = 1.67) is contained within a box whose volume is 2.0 m3. The pressure of the gas is 4.00 105 Pa. The total mass of the gas is 5.0 kg. Find the speed of sound in the gas.

4.) Hearing damage may occur when a person is exposed to a sound intensity level of 90.0 dB (relative to the threshold of hearing) for a period of 9.0 hours. One particular eardrum has an area of 2.30 10-4 m2. How much sound energy is incident on this eardrum during this time?

5.) A car is parked 20.0 m directly south of a railroad crossing. A train is approaching the crossing from the west, headed directly east at a speed of 50.0 m/s. The train sounds a short blast of its 290-Hz horn when it reaches a point 20.0 m west of the crossing. What frequency does the car's driver hear when the horn blast reaches the car? The speed of sound in air is 343 m/s. (Hint: Assume that only the component of the train's velocity that is directed toward the car affects the frequency heard by the driver.)

6.) A microphone is attached to a spring that is suspended from the ceiling, as the drawing indicates. Directly below on the floor is a stationary 436-Hz source of sound. The microphone vibrates up and down in simple harmonic motion with a period of 1.9 s. The difference between the maximum and minimum sound frequencies detected by the microphone is 2.2 Hz. Ignoring any reflections of sound in the room and using 343 m/s for the speed of sound, determine the amplitude of the simple harmonic motion.

Explanation / Answer

Q1.A=0.23 m

f=165 Hz

if the wave equation is y=A*sin(2*pi*f*t-2*pi*x*lambda)

at x=0, y=A(sin(2*pi*f*t)

similarly if wave equation is y=A*sin(2*pi*f*t+2*pi*x*lambda)

at x=0,y=A*sin(2*pi*f*t)

hence in both cases,y=0.23*sin(2*pi*165*t)

for y=0.2 ,

0.2=0.23*sin(2*pi*165*t)

==>sin(2*pi*165*t)=0.869565

==>2*pi*165*t=1.05432 radian, 2*pi+1.05432 radian and so on

so first instant , 2*pi*165*t=1.05432

==>t=1.01697 ms

for second instant, 2*pi*165*t=1.05432+2*pi

==>t=7.0775 ms

hence difference between two time instants=6.06053 ms

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