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Word Problems: Remember to Use GRASP and Show String Number Before Stating Final Answer. 1) Bats Produce Ultrasounds of Approximately

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Word Problems: Remember to use GRASP and show string number before stating final answer. 1) Bats produce ultrasounds of approximately 3.0times 10^4Hz If the time for the echo to return from a moth is 4.6times 10^-2s how many wavelengths are there between the bat and the moth? Assume a sound spoed of 340m/s. [Ans: 690] 2) A lightning flash is seen 8.0 s before the rumble of the thunder is heard. Find the distance to the lightning flash if the temperature is 21^circ C [Ans: 2800 m]

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Answer

**1) Wavelengths between bat and moth*** **Given:** * Frequency (f) = 3.0 x 10⁴ Hz * Time for echo (t) = 4.6 x 10⁻² s * Speed of sound (v) = 340 m/s* **Required:** * Number of wavelengths (n) between the bat and the moth* **Analysis:** * The total distance traveled by the sound wave is twice the distance between the bat and the moth (since it's an echo). * Distance = speed × time * Wavelength (λ) = speed / frequency * Number of wavelengths (n) = Total distance / Wavelength* **Solution:** 1. Time for sound to reach the moth (t_moth) = t / 2 = (4.6 x 10⁻² s) / 2 = 2.3 x 10⁻² s 2. Distance to the moth (d) = v × t_moth = 340 m/s × 2.3 x 10⁻² s = 7.82 m 3. Wavelength (λ) = v / f = 340 m/s / (3.0 x 10⁴ Hz) = 1.133 x 10⁻² m 4. Number of wavelengths (n) = d / λ = 7.82 m / (1.133 x 10⁻² m) ≈ 690* **Statement:** There are approximately 690 wavelengths between the bat and the moth.**2) Distance to the lightning flash*** **Given:** * Time delay (t) = 8.0 s * Temperature (T) = 21°C* **Required:** * Distance to the lightning flash (d)* **Analysis:** * The speed of sound in air depends on the temperature. We can approximate it using the formula: v ≈ 331.4 + 0.6T, where T is the temperature in Celsius. * Distance = speed × time* **Solution:** 1. Speed of sound (v) at 21°C: v ≈ 331.4 + 0.6 × 21°C = 331.4 + 12.6 = 344 m/s 2. Distance to the lightning flash (d) = v × t = 344 m/s × 8.0 s = 2752 m ≈ 2800 m (rounded to two significant figures)* **Statement:** The distance to the lightning flash is approximately 2800 m.