Home
/
Physics
/
An opera singer is facing the audience at the opera house, where the temperature is 23.5C. Her voice bounces off the back wall behind the audience and reaches a person sitting halfway between the singer and the back wall 1.45s after the sound is produced. a. Draw a diagram of the problem/situation Properly label the relevant distances. b. What is the distance (in meters)between the singer and the back wall?

Question

An opera singer is facing the audience at the opera house, where the temperature is 23.5C. Her voice bounces off the back wall behind the audience and reaches a person sitting halfway between the singer and the back wall 1.45s after the sound is produced. a. Draw a diagram of the problem/situation Properly label the relevant distances. b. What is the distance (in meters)between the singer and the back wall?

An opera singer is facing the audience at the opera house, where the temperature is
23.5C. Her voice bounces off the back wall behind the audience and reaches a person
sitting halfway between the singer and the back wall 1.45s after the sound is produced.
a. Draw a diagram of the problem/situation Properly label the relevant distances.
b. What is the distance (in meters)between the singer and the back wall?

Solution

expert verifiedExpert Verified
4.6(281 Voting)
avatar
LailaMaster · Tutor for 5 years

Answer

**a. Diagram:**<br /><br />```<br />Singer (S) Listener (L) Back Wall (W)<br /> |--------------------------x--------------------------|--------------------------x--------------------------|<br /> <---- x ----><br /> |--------------------------------------------------2x---------------------------------------------------|<br /><br />S = Singer's position<br />L = Listener's position (halfway between singer and wall)<br />W = Back Wall<br />x = Distance between Singer and Listener (also Listener and Wall)<br />2x = Total distance between Singer and Wall<br />```<br /><br />**b. Solution:**<br /><br />1. **Speed of sound:** The speed of sound in air depends on the temperature. The formula to calculate the speed of sound in air is approximately:<br /><br /> v = 331.4 + 0.6 * T<br /><br /> where v is the speed of sound in m/s, and T is the temperature in Celsius.<br /><br /> v = 331.4 + 0.6 * 23.5 = 345.5 m/s<br /><br />2. **Total distance traveled by sound:** The sound travels from the singer to the back wall and then back to the listener. Since the listener is halfway between the singer and the wall, the sound travels twice the distance between the singer and the listener. Let 'd' be the distance between the singer and the wall. The total distance the sound travels is 2d. Since the listener is halfway, the sound travels 'd' to the wall and 'd/2' back to the listener. However, the problem states the time is measured from when the sound is *produced* until it reaches the listener after reflecting off the back wall. Therefore, the total distance traveled by the sound is 'd' to the wall and 'd/2' back to the listener, for a total of 1.5d.<br /><br />3. **Calculation:** We know that distance = speed × time. We have the time (1.45 s) and the speed of sound (345.5 m/s). We can calculate the total distance traveled by the sound:<br /><br /> 1.5d = 345.5 m/s * 1.45 s<br /> 1.5d = 500.975 m<br /><br />4. **Distance between singer and wall:**<br /><br /> d = 500.975 m / 1.5 <br /> d ≈ 334 m<br /><br />Therefore, the distance between the singer and the back wall is approximately 334 meters.<br />
Click to rate: