This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Here are the solutions to the numerical problems: Q:1 A norm conversation involves sound intensities of about 3.0 × 10^-6 Wm^-2. What is the decibel level for this intensity? What is the intensity of the sound for 100dB. Step 1: Calculate the decibel level for the given intensity. The formula for sound intensity level in decibels () is: = 10 _10 ((I)/(I_0)) where I is the sound intensity and I_0 is the reference intensity (1.0 × 10^-12 Wm^-2). Given I = 3.0 × 10^-6 Wm^-2. Substitute the values: = 10 _10 (3.0 × 10^-6 Wm^-21.0 × 10^-12 Wm^-2) = 10 _10 (3.0 × 10^6) = 10 (_10 3.0 + _10 10^6) = 10 (0.4771 + 6) = 10 (6.4771) = 64.77 dB Step 2: Calculate the intensity of sound for 100 dB. Rearrange the formula to solve for I: I = I_0 × 10^/10 Given = 100 dB. Substitute the values: I = (1.0 × 10^-12 Wm^-2) × 10^100/10 I = (1.0 × 10^-12 Wm^-2) × 10^10 I = 1.0 × 10^-2 Wm^-2 The decibel level for 3.0 × 10^-6 Wm^-2 is 64.77 dB. The intensity of sound for 100 dB is 1.0 × 10^-2 Wm^-2. Q:2 At 100,000 how much current flows through your body if you touch your terminal of a 12 V battery? If your skin is wet, so that your resistance is only 1000 how much current would you receive from the same battery. Step 1: Calculate the current when resistance is 100,000 \ . Use Ohm's Law: I = (V)/(R) Given: V = 12 V, R = 100,000 \ . Substitute the values: I = 12 V100,000 \ I = 0.00012 A I = 0.12 mA Step 2: Calculate the current when resistance is 1000 \ . Given: V = 12 V, R = 1000 \ . Substitute the values: I = 12 V1000 \ I = 0.012 A I = 12 mA The current for 100,000 \ resistance is 0.12 mA. The current for 1000 \ resistance is 12 mA. Q:3 At a particular temperature, the speed of sound in air is 300 ms^-1. If the wavelength of a note is 5 cm, calculate the frequency of the sound wave. Is this frequency in the audible range of the human ear? Step 1: Convert the wavelength to meters. Given: = 5 cm. 5 cm = 5 × 10^-2 m = 0.05 m Step 2: Calculate the frequency of the sound wave. The relationship between speed, frequency, and wavelength is v = f . Rearrange to solve for frequency f = (v)/(). Given: v = 300 ms^-1, = 0.05 m. Substitute the values: f = 300 ms^-10.05 m f = 6000 Hz Step 3: Determine if the frequency is in the audible range. The audible range for human hearing is typically 20 Hz to 20,000 Hz. Since 6000 Hz falls within this range, it is audible. The frequency of the sound wave is 6000 Hz. Yes, this frequency is in the audible range of the human ear. Q:4 By applying a potential Difference of 1p V across a conductor a current of 1.5 A passes through it. How much energy would be obtain from the current in 2 minutes? Step 1: Convert potential difference and time to standard units. Given: Potential difference V = 1 pV (picoVolt). 1 pV = 1 × 10^-12 V Given: Time t = 2 minutes. 2 minutes = 2 × 60 s = 120 s Given: Current I = 1.5 A. Step 2: Calculate the energy obtained. The formula for electrical energy (E) is E = V I t. Substitute the values: E = (1 × 10^-12 V) × (1.5 A) × (120 s) E = 1.5 × 120 × 10^-12 J E = 180 × 10^-12 J E = 1.8 × 10^-10 J The energy obtained from the current in 2 minutes is 1.8 × 10^-10 J.