A marine survey ship sends a sound wave straight to the seabed. It receives an echo 1.5 s later. The speed of sound in sea water is 150p ms⁻¹. Find the depth of the sea at this position.

Here are the solutions to the numerical problems: Q:5 A marine survey ship sends a sound wave straight to the seabed. It receives an echo 1.5 s later. The speed of sound in sea water is 150p ms⁻¹. Find the depth of the sea at this position. Step 1: Identify the given values and clarify the speed of sound. Given: Time for echo, t = 1.5 s Speed of sound, v = 150 p ms^-1. The unit "p" (pico) means 10^-12. A speed of 150 × 10^-12 ms^-1 is extremely slow and unrealistic for sound in seawater. Sound in seawater is typically around 1500 ms^-1. Assuming "150p" is a typo and it should be 1500 ms^-1 (or possibly 150 ms^-1 if it's a very specific context, but 1500 ms^-1 is standard for seawater). We will proceed with v = 1500 ms^-1. Step 2: Calculate the depth of the sea. The sound travels to the seabed and back, so the total distance covered is 2 × depth. The formula for distance is d = v × t. So, 2 × depth = v × t. depth = (v × t)/(2) Substitute the values: depth = 1500 ms^-1 × 1.5 s2 depth = 2250 m2 depth = 1125 m The depth of the sea at this position is 1125 m. Q:6 An electric bulb is marked with 220V, 100W. Find the resistance of the filament of the bulb. If the bulb is used 5 hours daily, find the energy in Kilowatt hour consumed by the bulb in one month ( 30 Days) Step 1: Find the resistance of the filament. Given: Voltage, V = 220 V Power, P = 100 W The formula relating power, voltage, and resistance is P = (V^2)/(R). Rearrange to solve for R: R = (V^2)/(P). Substitute the values: R = (220 V)^2100 W R = 48400 V^2100 W R = 484 \ Step 2: Find the energy consumed in one month (30 days). Given: Power, P = 100 W Daily usage, t_daily = 5 hours Number of days, N = 30 days First, convert power to kilowatts: P_kW = 100 W = 0.1 kW. Next, calculate the total time of usage in hours for one month: T_total = t_daily × N = 5 hours/day × 30 days = 150 hours The formula for energy consumed is E = P_kW × T_total. Substitute the values: E = 0.1 kW × 150 hours E = 15 kWh The resistance of the filament is 484 \ . The energy consumed by the bulb in one month is 15 kWh. Q:7 A sound waves has frequency of 2 kHz and wavelength 35 cm. How long will it take to travel 1.5 km? Step 1: Convert given values to standard units. Given: Frequency, f = 2 kHz = 2 × 1000 Hz = 2000 Hz Wavelength, = 35 cm = 0.35 m Distance, d = 1.5 km = 1.5 × 1000 m = 1500 m Step 2: Calculate the speed of the sound wave. The relationship between speed (v), frequency (f), and wavelength () is v = f . Substitute the values: v = 2000 Hz × 0.35 m v = 700 ms^-1 Step 3: Calculate the time taken to travel the given distance. The formula for time (t) is t = (d)/(v). Substitute the values: t = 1500 m700 ms^-1 t ≈ 2.14 s It will take approximately 2.14 s to travel 1.5 km. Q:8 A current of 3mA is flowing through a wire for 1 minutes. What is the charge flowing through the wire? Step 1: Convert given values to standard units. Given: Current, I = 3 mA = 3 × 10^-3 A Time, t = 1 minute = 60 s Step 2: Calculate the charge flowing through the wire. The formula for charge (Q) is Q = I × t. Substitute the values: Q = (3 × 10^-3 A) × (60 s) Q = 180 × 10^-3 C Q = 0.18 C The charge flowing through the wire is 0.18 C. Q:9 If at Anarkali Bazar Lahore, the intensity level of sound is 80 dB, what will be the intensity of sound there? Step 1: Identify the given values and the formula for intensity. Given: Sound intensity level, = 80 dB Reference intensity, I_0 = 1.0 × 10^-12 Wm^-2 (standard value) The formula for sound intensity level is = 10 _10 ((I)/(I_0)). To find I, rearrange the formula: ()/(10) = _10 ((I)/(I_0)) 10^/10 = (I)/(I_0) I = I_0 × 1