Who will hear the voice of a singer first-a person in the balcony 50 m away from the stage (Fig. 22-19), or a person 2000 km away at home whose ear is next to the radio? Assume that the microphone is a few centimeters from the singer and the temperature is 20°C.
The answer will depend upon whether the radio is connected via the internet or satellite radio, and whether the station uses electronic signal delay to edit profanity. Many do.
If these possibilities are ignored, the time for the sound to get to the listener from the stage is
50 m/340 m/s = 0.147 s
and the time for the radio signal to arrive from 2000 km away is
2000 km/3*10^5 km/s = 0.0067 s
The radio listener therefore hears the singer first, in this situation.
The time delay for the sound to reach the microphone applies to both listeners, and does not affect the answer.
Well, let me tell you a joke to lighten the mood before we get into the physics of sound travel. Why don't scientists trust atoms? Because they make up everything!
Alright, now let's talk about the singer's voice. Sound travels at approximately 343 meters per second in dry air at 20°C.
The person in the balcony 50 meters away from the stage will hear the voice of the singer almost instantly. The time it takes for sound to travel 50 meters is very small, so we can say that they hear it practically in real-time.
On the other hand, the person 2000 km away at home, whose ear is next to the radio, will experience a delay in hearing the singer's voice. To estimate the time it takes for sound to travel 2000 km, we need to divide the distance by the speed of sound.
So, 2000 km divided by 343 m/s gives us roughly 5825 seconds or around 1.6 hours. That's quite a long wait!
Therefore, the person in the balcony 50 meters away from the stage will hear the singer's voice first, long before the person 2000 km away. But hey, at least the person at home can dance around and pretend to be their own concert in the meantime!
To determine who will hear the voice of a singer first - the person in the balcony or the person at home next to the radio - we need to consider the speed of sound and the distance between each person and the singer.
On a general basis, sound travels through air at a speed of approximately 343 meters per second at a temperature of 20°C. This speed may vary slightly depending on factors such as humidity and air pressure, but we will assume the standard value for this calculation.
1. Person in the balcony:
The person in the balcony is 50 meters away from the stage. The sound produced by the singer will travel through the air and reach this person. To calculate the time it takes for the sound to reach the person in the balcony, we can use the formula: time = distance / speed.
Distance = 50 meters
Speed = 343 meters per second (approximate)
Time = 50 meters / 343 meters per second ≈ 0.146 seconds
Therefore, the person in the balcony will hear the voice of the singer after approximately 0.146 seconds.
2. Person at home next to the radio:
The person at home is 2000 km away from the stage. However, instead of the sound traveling directly from the stage to the person, it will be transmitted through the radio waves and then played on the person's radio. Since radio waves travel at the speed of light, their speed is significantly faster than sound.
To simplify the calculation, we will assume that the time it takes for the radio waves to travel from the stage to the person's home is negligible. Therefore, the time it takes for the person at home to hear the voice of the singer will be determined by the time it takes for the sound to travel from the radio to the person's ear.
Assuming the person's ear is next to the radio, the sound will travel through the air (neglecting any time delay within the radio or other factors). Using the same speed of sound, we can calculate the time as follows:
Distance = 0 meters (assuming the person's ear is right next to the radio)
Speed = 343 meters per second (approximate)
Time = 0 meters / 343 meters per second = 0 seconds
Therefore, the person at home, with their ear next to the radio, will hear the voice of the singer almost instantaneously.
In conclusion, the person at home, with their ear next to the radio, will hear the voice of the singer first.
To determine who will hear the voice of the singer first, we need to consider the speed of sound and the distance of each listener from the source of the sound.
The speed of sound in air at 20°C is approximately 343 meters per second.
Let's calculate the time it takes for the sound to reach each listener.
For the person in the balcony, who is 50 meters away from the stage:
Time = Distance / Speed
Time = 50 meters / 343 meters per second
Time ≈ 0.146 seconds
For the person 2000 km away at home:
Convert 2000 km to meters: 2000 km * 1000 meters per kilometer = 2,000,000 meters.
Time = Distance / Speed
Time = 2,000,000 meters / 343 meters per second
Time ≈ 5820.23 seconds
Comparing the times, we see that the person in the balcony will hear the voice of the singer first because it takes them approximately 0.146 seconds, while it would take the person at home approximately 5820.23 seconds (or about 1 hour and 37 minutes) to hear the same sound through the radio.
Therefore, the person in the balcony 50 meters away from the stage will hear the voice of the singer first.