A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.20 s after shouting. How long (in meters) is the lake?
speed of sound there? Call it v
(maybe around 350 m/s)
goes twice L
2 L = v T = 2.2 v
L = 1.1 v
The string on a violin has a fundamental frequency of 150.0 Hz. The length of the vibrating portion is 36 cm and has a mass of 0.51 g. Under what tension (in newtons) must the string be placed?
I have showed you how to do these.
speed = sqrt (T/u)
u = mass/length
distance for wave to travel in one period = 2L (because half a wave is fundamental)
T = distance/speed
frequency = 1/T
To determine the length of the lake, we can use the fact that the time it takes for the sound to travel to the cliff and back is twice the time it takes for the hiker to hear the echo.
Let's start by finding the time it takes for the sound to travel to the cliff. Since sound travels at a speed of approximately 343 meters per second in air, we can use the formula:
distance = speed * time
The time it takes for the sound to travel to the cliff is half of the total time, as the sound needs to travel to the cliff and then back to the hiker. So we can calculate the distance to the cliff using:
distance_to_cliff = (speed_of_sound * time_to_hear_echo) / 2
Given that the hiker hears the echo 2.20 seconds after shouting, we can substitute the values into the equation:
distance_to_cliff = (343 m/s * 2.20 s) / 2
distance_to_cliff = 377.65 meters
Since the sound had to travel from the hiker to the cliff and then back again, the total distance covered is twice the distance to the cliff. Therefore, we can calculate the total length of the lake:
length_of_lake = 2 * distance_to_cliff
length_of_lake = 2 * 377.65 meters
length_of_lake = 755.3 meters
Therefore, the length of the lake is approximately 755.3 meters.