How long will it take an echo to return across a canyon that is 61.0 m from one side to the other if the temperature is 25 C?
Hint: Find out what is the speed of sound in 25 C air.
To calculate the time it takes for an echo to return across a canyon, we need to know the speed of sound in air at the given temperature.
The speed of sound in air can be calculated using the following formula: v = 331.4 + 0.6T
Where:
v is the speed of sound in meters per second (m/s)
T is the temperature in degrees Celsius (°C)
Substituting the given temperature of 25 °C into the formula, we have:
v = 331.4 + 0.6(25)
v = 331.4 + 15
v = 346.4 m/s
Now that we have the speed of sound, we can calculate the time it takes for the sound to travel across the canyon.
Using the formula: time = distance / speed
Substituting the given distance of 61.0 m and the calculated speed of sound of 346.4 m/s into the formula, we have:
time = 61.0 / 346.4
time ≈ 0.176 s
Therefore, it would take approximately 0.176 seconds for the echo to return across the canyon.
To calculate the time it will take for an echo to return across a canyon, we need to know the speed of sound and the distance across the canyon.
The speed of sound depends on the temperature of the air. It increases with higher temperature because the air molecules move faster. The formula to calculate the speed of sound in dry air is given by:
v = 331.3 + 0.606 * T
where v is the speed of sound in meters per second and T is the temperature in degrees Celsius.
In this case, the temperature is given as 25°C. Plugging in this value into the formula, we get:
v = 331.3 + 0.606 * 25
v = 331.3 + 15.15
v = 346.45 m/s (approximately)
Now that we have the speed of sound, we can calculate the time it will take for the echo to travel across the canyon. The time is equal to the distance divided by the speed, given by:
t = d / v
where t is the time in seconds, d is the distance in meters, and v is the speed of sound in meters per second.
In this case, the distance across the canyon is given as 61.0 m. Plugging in this value and the speed of sound we calculated, we get:
t = 61.0 / 346.45
t = 0.176 seconds (approximately)
Therefore, it will take approximately 0.176 seconds for the echo to return across the canyon at a temperature of 25°C.